U.S. patent application number 10/636318 was filed with the patent office on 2004-07-01 for high temperature superconducting cabon nanotubes and methods for making them.
Invention is credited to Zhao, Guo-meng.
Application Number | 20040126304 10/636318 |
Document ID | / |
Family ID | 31715722 |
Filed Date | 2004-07-01 |
United States Patent
Application |
20040126304 |
Kind Code |
A1 |
Zhao, Guo-meng |
July 1, 2004 |
High temperature superconducting cabon nanotubes and methods for
making them
Abstract
Disclosed are high temperature and/or room temperature
superconducting carbon nanotube compositions having either a
critical doping range, a critical chirality or a mixture thereof,
high temperature superconducting graphite compositions having a
critical doping range, methods of achieving a phase-coherent, near
zero resistivity superconducting state in multiwalled carbon
nanotubes and bundles of superconducting carbon nanotubes, methods
of achieving a large positive magnetoresistance in bundles of
superconducting carbon nanotubes, and methods for making and using
such nanotubes or bundles. Disclosed also are devices and
apparatuses (e.g., magnetic reading heads, magnetic switch devices,
magnetic imaging devices, and superconducting quantum interference
devices) comprising superconducting carbon nanotubes and/or bundles
of superconducting carbon nanotubes.
Inventors: |
Zhao, Guo-meng; (Hacienda
Heights, CA) |
Correspondence
Address: |
ROBERT W STROZIER, P.L.L.C
PO BOX 429
BELLAIRE
TX
77402-0429
US
|
Family ID: |
31715722 |
Appl. No.: |
10/636318 |
Filed: |
August 7, 2003 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60401696 |
Aug 7, 2002 |
|
|
|
Current U.S.
Class: |
423/447.2 ;
257/E39.008; 505/100 |
Current CPC
Class: |
B82Y 10/00 20130101;
C04B 2235/96 20130101; C04B 35/52 20130101; C04B 2235/94 20130101;
C04B 2235/5288 20130101; B82Y 30/00 20130101; H01L 39/005
20130101 |
Class at
Publication: |
423/447.2 ;
505/100 |
International
Class: |
D01F 009/12; C10F
005/00 |
Claims
I claim:
1. A composition comprising at least one nanotube, where the at
least one nanotube has a phase-coherent or phase incoherent
superconductivity above 20 K.
2. The composition of claim 1, wherein the superconductivity occurs
above 120 K.
3. The composition of claim 1, wherein the superconductivity occurs
above 250 K.
4. The composition of claim 1, wherein the superconductivity occurs
above 300 K.
5. The composition of claim 1, wherein the nanotubes are selected
from the group consisting of single-wall nanotubes, multi-walled
nanotubes and mixtures or combinations thereof.
6. The composition of claim 2, wherein the nanotubes are single
walled nanotubes and the superconductivity is phase-incoherent.
7. The composition of claim 2, wherein the nanotubes are
multi-walled nanotubes and the superconductivity is
phase-coherent.
8. The composition of claim 1, further comprising a bundle of
nanotubes.
9. The composition of claim 8, wherein the nanotubes are selected
from the group consisting of single-wall nanotubes, multi-walled
nanotubes and mixtures or combinations thereof.
10. The composition of claim 9, wherein the nanotubes are single
walled nanotubes and the superconductivity is phase-coherent.
11. The composition of claim 9, wherein the nanotubes are
multi-walled nanotubes and the superconductivity is
phase-coherent.
12. The composition of claim 1, further comprising a matrix
including bundles of nanotubes.
13. The composition of claim 12, wherein the nanotubes are selected
from the group consisting of single-wall nanotubes, multi-walled
nanotubes and mixtures or combinations thereof.
14. The composition of claim 13, wherein the nanotubes are single
walled nanotubes and the superconductivity is phase-coherent.
15. The composition of claim 13, wherein the nanotubes are
multi-walled nanotubes and the superconductivity is
phase-coherent.
16. The composition of claim 1, further comprising nanotubes,
nanotube bundles or mixtures or combinations thereof.
17. The composition of claim 1, wherein the nanotubes are capable
of conducting current with minimal to no loss.
18. The composition of claim 1, wherein each nanotube includes an
outer wall having a chirality of Mod3(n-m)=0.
19. The composition of claim 1, wherein each nanotube includes an
outer wall having a chirality of n-m=0.
20. The composition of claim 8, wherein each wall of each nanotube
has a chirality of Mod3(n-m)=0.
21. The composition of claim 8, wherein each wall of each nanotube
has a chirality of n-m=0.
22. The composition of claim 8, wherein the nanotubes are aligned
along an axis and an inter-nanotube separation is between about 2.2
.ANG. and about 5 .ANG..
23. The composition of claim 8, wherein the nanotubes are aligned
along an axis and an inter-nanotube separation is between about
2.5.ANG. and about 4 .ANG..
24. The composition of claim 8, wherein the nanotubes are aligned
along an axis and an inter-nanotube separation is between about 2.5
.ANG. and about 3.5 .ANG..
25. The composition of claim 8, wherein the nanotubes are aligned
along an axis and an inter-nanotube separation is between about
2.75 .ANG. and about 3.25 .ANG..
26. The composition of claim 1, wherein the composition is formed
into an electrically conducting element, a rope, or a wire.
27. The composition of claim 1, wherein the composition is
deposited on a metallic surface.
28. The composition of claim 1, further comprising sufficient
dopant to support superconductivity.
29. The composition of claim 28, wherein the dopant is selected
from the group consisting of a surface having a different work
function, an electric field, a chemical dopant, and a physical
dopant.
30. The composition of claim 1, wherein the chemical and physical
dopants are selected from the group consisting of oxidants,
reductants, dopants resulting from atom or ion implantation, and
dopants from charged particle bombardment.
31. An apparatus comprising a component including a composition
claims 1-30.
32. The apparatus of claim 31, further comprising at least two
electronic components interconnected with the composition.
33. The apparatus of claim 31, wherein the apparatus comprises a
levitation apparatus comprising superconducting magnets comprising
the composition.
34. The apparatus of claim 31, wherein the component includes an
electrically conductive element.
35. The apparatus of claim 31, wherein the apparatus comprises
magnetic reading heads, magnetic switch devices, magnetic imaging
devices or superconducting quantum interference devices.
36. A method for forming superconducting materials comprising the
steps of: providing a composition including superconducting
nanotubes, superconducting nanotube bundles or mixtures or
combinations thereof, aligning the superconducting nanotubes,
superconducting bundles or mixtures or combinations thereof and
forming the aligned superconducting nanotubes, superconducting
nanotube bundles or mixtures or combinations thereof into an
elongate form.
37. The method of claim 36, further comprising the step of: doping
the elongate form with sufficient dopant so that the form
superconducts at a desired temperature.
38. The method of claim 36, the desired temperature is above 20
K.
39. The method of claim 36, the desired temperature is above 120
K.
40. The method of claim 36, the desired temperature is above 250
K.
41. The method of claim 36, the desired temperature is above 300
K.
42. A method for forming superconducting materials comprising the
steps of: providing a suspension of a composition including
superconducting nanotubes, superconducting nanotube bundles or
mixtures or combinations thereof in a solvent; and forcing the
suspension through an small orifice onto a substrate, where the
forcing cause an alignment of the superconducting nanotubes,
superconducting bundles or mixtures or combinations thereof on the
substrate.
43. A method for forming superconducting connection between
electronic contacts comprising the steps of: providing a suspension
of a composition including superconducting nanotubes,
superconducting nanotube bundles or mixtures or combinations
thereof; and spraying the suspension onto a substrate having
electronic contacts disposed thereon so that the composition forms
an electrically conductive pathway between a desired pair of
contact along a desired path, where the spraying aligns the
superconducting nanotubes, superconducting bundles or mixtures or
combinations thereof.
Description
RELATED APPLICATIONS
[0001] This application claims provisional priority to U. S.
Provisional Patent Application Serial No. ______, filed 7 Aug.
2002.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] The present invention relates to the general field of
superconductivity, material science, and engineering. This
invention relates particularly to low dissipation or
dissipation-free electrical transport and the Meissner effect above
room temperature in high temperature superconducting nanotubes and
to the method for making and using same.
[0004] More particularly, the present invention relates to high
temperature superconducting carbon nanotube compositions having
either a critical doping range, a critical chirality or a mixture
thereof, to compositions comprising single-walled nanotubes,
multi-walled nanotubes, or mixtures or combination thereof and to
compositions comprising bundles of the aligned nanotubes, to
methods of using aligned nanotube bundles, to wires or other
conductors of electricity including superconducting carbon
nanotubes and aligned nanotube bundles, to methods of making and
using same, and methods to achieve a phase-coherent, near zero
resistivity superconducting state in superconducting nanotubes; to
methods of achieving a large positive magnetoresistance in bundles
of superconducting carbon nanotubes; to magnetic reading heads
comprising superconducting carbon nanotubes; to magnetic switch
devices comprising superconducting carbon nanotubes; to magnetic
imaging devices comprising superconducting carbon nanotubes; to
superconducting quantum interference devices comprising
superconducting carbon nanotubes. Many features of the materials
including carbon nanotubes are a consequence of coherent (phase
locked) superconductivity in carbon nanotubes that persist at
temperatures even well above room temperature.
[0005] 2. Description of the Related Art
[0006] Superconductivity is a phenomenon displayed by certain
conductors that demonstrate no resistance to the flow of an
electric current. Superconductors also repel magnetic fields
(Meissner effect). Superconductors have the ability to conduct
electricity without the loss of energy. When current flows in an
ordinary conductor, for example copper wire, some energy is lost.
In a light bulb or electric heater, the electrical resistance
creates light and heat. In metals such as copper and aluminum,
electricity is conducted as outer energy level electrons migrate as
individuals from one atom to another. These atoms form a vibrating
lattice within the metal conductor; the warmer the metal the more
it vibrates. As the electrons begin moving through the maze, they
collide with tiny impurities or imperfections in the lattice or
lattice vibrations. When the electrons bump into these obstacles
they fly off in all directions and lose energy in the form of
heat.
[0007] Inside a superconductor, the behavior of electrons is vastly
different. The impurities and lattice are still there, but the
movement of the superconducting electrons through the obstacle
course is quite different. As the superconducting electrons travel
through the conductor they pass unobstructed through the complex
lattice. Because they bump into nothing and create no friction they
can transmit electricity with no appreciable loss in the current
and no loss of energy.
[0008] The ability of electrons to pass through superconducting
material unobstructed has puzzled scientists for many years. The
warmer a substance is the more it vibrates. Conversely, the colder
a substance is the less it vibrates. Early researchers suggested
that fewer atomic vibrations would permit electrons to pass more
easily. However this predicts a slow decrease of resistivity with
temperature. It soon became apparent that these simple ideas could
not explain superconductivity. It is much more complicated than
that.
[0009] Superconductivity is manifested only below a certain
critical temperature called "T.sub.c" and a critical magnetic field
called "H.sub.c," which vary with the material used. Before about
1986, the highest T.sub.c that could be achieved was 23.2 K
(-249.8.degree. C./-417.6.degree. F.) in niobium-germanium
compounds. Such low temperatures were achieved by use of liquid
helium, an expensive, inefficient coolant. Ultralow-temperature
operations place a severe constraint on the overall efficiency of a
superconducting machine. Thus, large-scale operation of such
machines has not been considered practical.
[0010] Following about 1986, discoveries began to radically alter
the situation. Ceramic copper-oxide compounds containing rare earth
elements were found to be superconductive at temperatures high
enough to permit using liquid nitrogen as a coolant. Because liquid
nitrogen, at 77 K (-196.degree. C./-321.degree. F.), cools 20 times
more effectively than liquid helium and is 10 times less expensive,
a variety of possible applications suddenly began to hold the
promise of economic feasibility. In about 1987, the composition of
one of these superconducting compounds, with a T.sub.c of 94 K
(-179.degree. C./-290.degree. F.), was revealed to be
YBa.sub.2Cu.sub.3O.sub.7 (yttrium-barium-copper-oxide). It has
since been shown that rare-earth elements, such as yttrium, are not
an essential constituent, and in about 1988, a
thallium-barium-calcium copper oxide was discovered with a T.sub.c
of 125 K (-148.degree. C./-234.degree. F.).
[0011] Because of their lack of resistance, superconductors have
been used to make electromagnets that generate large magnetic
fields with no energy loss. Superconducting magnets have been used
in diagnostic medical equipment, studies of materials, and in the
construction of powerful particle accelerators. Using the quantum
effects of superconductivity, devices have been developed that
measure electric current, voltage, and magnetic field with
unprecedented sensitivity. The discovery of better superconducting
compounds is an important step toward a far wider spectrum of
applications, including faster computers with larger storage
capacities, nuclear fusion reactors in which ionized gas is
confined by magnetic fields, magnetic levitation (lifting or
suspension) of high-speed ("Maglev") trains, and perhaps most
important of all, more efficient generation and transmission of
electric power.
[0012] Although some cuprate systems are known to superconduct at
temperature as high as 130 K, the ultimate goal of research into
high temperature superconductors is to find materials that
superconduct at or above room temperature (.about.300 K). Thus,
there is a need in the art for stable, easy to make and
commercially viable room temperature (RT) superconducting
materials. Nevertheless, finding RT superconductors is a very
challenging problem in science. It was theoretically shown that RT
superconductivity can not be realized within the conventional
phonon-mediated pairing mechanism. On the other hand, a theoretical
calculation showed that superconductivity as high as 500 K can be
reached through a pairing interaction mediated by undamped acoustic
plasmon modes in a quasi-one-dimensional electronic system.
Moreover, high-temperature superconductivity can occur in a
multi-layer electronic system due to an attraction of charge
carriers in the same conducting layer via exchange of virtual
plasmons in neighboring layers. If these theoretical studies are
relevant, one should be able to find high-temperature
superconductivity in quasi-one-dimensional (1D) and/or multi-layer
systems.
[0013] Carbon nanotubes (discovered in 1991) constitute a novel
class of quasi-one-dimensional materials, which would offer the
potential for high-temperature superconductivity. The simplest
single walled nanotube (SWNT) consists of a single graphite sheet
that is curved into a long cylinder, with a diameter which can be
smaller than 1 nm. Band-structure calculations predict that carbon
nanotubes have two types of electronic structures depending on the
chirality, which is indexed by a chiral vector (n,m): n-m=3N+.nu.,
where N, n, m are the integers, and .nu.=0, .+-.1. The tubes with
.nu.=0 are metallic while the tubes with .nu.=.+-.1 are
semiconductive. The multi-walled nanotubes consist of at least two
concentric shells which could have different chiralities. The MWNTs
possess both quasi-one-dimensional and multi-layer electronic
structures. This unique quasi-one-dimensional electronic structure
in both SWNTs and MWNTs makes them ideal for plasmon-mediated
high-temperature superconductivity.
[0014] Indeed, in a series of five papers resident on the cond-mat
e-print archive since November 2001 (cond-mat/0111268;
cond-mat/0208197; cond-mat/0208198; cond-mat/0208200;
cond-mat/0208201), the inventor provides over twenty arguments for
room temperature superconductivity in carbon nanotubes. The
one-dimensionality of the nanotubes complicates the
right-of-passage for prospective quasi-one-dimensional
superconductors. The Meissner effect is less visible because the
diameters of nanotubes are much smaller than the penetration depth.
Zero resistance is less obvious because of the quantum contact
resistance and significant quantum phase slip, both of which are
associated with a finite number of transverse conduction channels.
Nonetheless, on-tube resistance at room temperature has been found
to be indistinguishable from zero for many individual multi-walled
nanotubes.
[0015] It is known that the superconducting fluctuation in
one-dimensional (1D) superconductors plays an essential role in the
resistivity transition. A number of experiments have demonstrated a
large resistance well below T.sub.c in thin superconducting
wires.
[0016] Theories based on the quantum phase slips (QPS) can explain
the finite resistance in 1D superconductors. Essentially, the phase
slips at low temperatures are related to the macroscopic quantum
tunneling (MQT), which allows the phase of the superconducting
order parameter to fluctuate between zero and 2.pi. at some points
along the wire, resulting in voltage pulses. The QPS tunneling rate
is proportional to exp (-S.sub.QPS), where S.sub.QPS, in clean
superconductors, is very close to the number of transverse channels
N.sub.Ch in the limit of weak damping. If the number of the
transverse channels N.sub.Ch is small, the QPS tunneling rate is
not negligible, leading to a finite resistance at low temperatures.
For a single-walled nanotube (SWNT), N.sub.Ch=2, implying a large
QPS tunneling rate and thus a large resistance even if it is a
superconductor. For MWNTs with several metallic layers adjacent to
each other, the number of the transverse channels will increase
substantially, resulting in the suppression of the QPS. If two
superconducting tubes are closely packed together to effectively
increase the number of the channels, one would find a small
resistance at room temperature if the constituent tubes have a
mean-field T.sub.c0 well above room temperature. This can naturally
explain why on-tube resistance at room temperature has been found
to be indistinguishable from zero for many individual multi-walled
nanotubes. This also provides an essential theoretical ground for
developing arts to realize coherent, non-dissipative, and stable
room temperature superconductivity in carbon nanotubes.
[0017] Definitions
[0018] Quantum phase slips are phenomena in which the phase
coherence is momentarily broken at some point in the
superconductor, allowing a phase slip to occur before phase
coherence is reestablished.
[0019] Quasi-one-dimensional superconductors are superconductors
with transverse dimension far smaller than the superconducting
coherent length or superconductors where the electrons essentially
move along one direction.
[0020] Mean-field superconducting transition temperature is the
critical temperature below which the electron pairing starts to
take place.
[0021] Phase coherent superconducting state: A state with
resistance approaching zero.
[0022] Phase incoherent superconducting state: Finite-resistance
state below the mean-field superconducting temperature.
[0023] Meissner effect is a unique phenomenon of a superconductor:
A magnetic field can be expelled from the bulk of a superconductor
when the field is cooled from a temperature above the
superconducting transition temperature.
[0024] Josephson coupling: Two superconducting materials that are
separated by an insulating or normal metal layer, or by a short,
narrow constriction can have a phase coherence between the two
superconducting materials.
[0025] A nanotube is a small tube having a diameter between about
0.42 and about 1000 nanometers.
[0026] A carbon nanotube (CNT) is a nanotube comprising
substantially elemental carbon.
[0027] A multiwalled carbon nanotube (MWNT) is a collection of
nested CNTs which share a common axis.
[0028] A single walled carbon nanotube (SWNT) is a CNT comprising
only one shell or layer.
[0029] A superconducting carbon nanotube (SCNT) is a CNT that
superconducts.
[0030] Doping is the process by which the electronic carrier
density is changed. Doping alters the overall electrical transport
behavior. Like cuprate superconductors which can be doped into the
superconducting state or non-superconducting state, SCNTs can be
doped to be optimally doped superconductors, non-optimally doped
superconductors or to be non-superconductors.
[0031] CNTs can either have a metallic or a semiconducting
chirality. If (n-m) mod 3=0, the tube is said to have a metallic
chirality. Otherwise the tube's chirality is semiconducting.
Technically, non-armchair metallic chirality tubes have a small gap
making them semiconducting. However, this gap is small. Because the
Fermi level can easily be doped outside this small gap, the
inventor ignores the semiconducting behavior in this tube.
[0032] Both semiconducting and metallic chirality CNTs can be made
to superconduct via the doping of carriers into the CNT.
[0033] Superconducting tubes are quasi-1D superconductors and can
be Josephson coupled to exhibit less dissipation or
resistivity.
[0034] Semiconducting tubes have a semiconducting chirality and
have the Fermi level between the valence and conduction band
edge.
[0035] A straight CNT is parallel to another straight CNT, if the
two CNTs are aligned along the same direction. Such tubes will have
a length l in common, where l is the minimum of the length of both
tubes laid side-by-side. Over the distance l, one CNT will have
analogous points that are separated from analogous points on the
second CNT, by the same or nearly the same distance.
[0036] A CNT is proximate to another CNT, if the two CNTs are close
to each other. Proximity increases as more points on one CNT become
closer to nearest points on the other CNT. For two straight CNTs
which share a length l, proximity is maximized when the CNTs are
parallel. Further, if a difference in tube diameter s exceeds about
0.68 nm, the tubes will exhibit the greatest proximity if the tubes
are nested over 1, i.e., the smaller tube is inside the larger
tube. If the difference in tube diameters for two SWNTs is less
than about 0.68 nm, it may not be possible to nest the tubes and
proximity is maximized if the tubes are parallel and in contact
over the length l.
[0037] Maximal proximity means CNTs arranged parallel with an
optimal or minimized distance d between analogous points on the
parallel disposed CNTs, i.e., d represents a minimized distance
between analogous points on the parallel disposed CNTs. Such
superconducting tubes are said to be maximally proximate
superconducting carbon nanotubes (MPSCNTs). A plurality or
collection of CNTs are `maximally proximate` when each tube is
maximally proximate each of its nearest neighbors. When the concept
of maximal proximity is directed to collections of tubes, then
macro-conductive structures can be constructed. Because of the
finite length of a CNT, one CNT can begin near or before another
CNT ends. Thus percolation can arise from intertube coupling and
create a macroscopic continuity even though the CNTs themselves are
of a microscopic dimension.
[0038] If such proximate tubes are jointly shaped so that the tubes
have the same or similar separation along every point, but are not
aligned in a straight line, then these tubes are also said to be
parallel.
[0039] A coherent superconducting carbon nanotube line (CSCNTL) is
a collection of superconducting carbon nanotubes (SCNTs) which
exhibits a greater "phase coherence" (compared to the separated
tubes) and therefore a lower resistivity than exhibited by the
separated tubes. MPSCNTs comprises a CSCNTL. For example, the
collection of CNTs comprises CNTs of equal or nearly equal length
where the ends of the tubes only are in electrical contact with
each other. The net resistance of the collection is smaller if the
SCNTs are closer to each other. Proximity induces this
superconducting synergy. The phase coherence is a result of
Josephson coupling between individual SCNTs that causes the net
resistance of two adjacent SCNTs to be less than the parallel
combination of their separated resistance.
[0040] This proximity induced synergy in SCNTs results in the
formation of collections of SCNTs having a very low resistivity. A
dc resistivity of less than 1 .mu.Ohm-cm is readily obtainable in
aligned collections of SCNTs. Thus, increasing the number of SCNTs
that have maximal proximity in a collection of SCNTs results in
more coherent superconducting transport within the construct.
Although individual superconducting SWNTs are not entirely phase
coherent and therefore exhibit appreciable dissipation, when
bundled together the collective resistance is much less than the
resistance found from an end to end combination of individual
tubes. The greater the number of SCNTs that have maximal proximity
in the collection, the greater the number of conductive channels,
and, therefore, the lower the contact resistance. Moreover, the
more maximally proximate SCNTs in the collection, the lower the
collective and individual on-tube resistances. The net resistance
decreases as both the contact and on-tube resistances decrease.
[0041] Individual SCNTs, especially individual single-walled carbon
nanotubes (SWCNTs), can exhibit a large amount of phase slip
resistivity. The resistivity of these individual SWCNTs can change
significantly when the SWCNTs are brought into maximal proximity
during the construction of SCNTLs or CSCNTLs.
[0042] The term orphan superconducting carbon nanotube (OSCNT)
means any SCNT having a resistivity that lowers appreciable when
brought into maximal proximity with another SCNT or superconductor.
Thus, SCNTs are either CSCNTs or OSCNTs. The distinction between an
CSCNT and OSCNT is rather qualitative, but the distinction is
evidenced from a relative change in superconducting properties as
the isolated SCNT in question is brought close to an isolated
CSCNT. An OSCNT is therefore distinguished from a CSCNT because an
OSCNT exhibits a larger relative change in resistivity when brought
near an CSCNT as compared to the change in resistivity when an
CSCNT is brought near another CSCNT. For example, the resistivity
of an OSCNT maybe reduced as much as about 60%, while the
resistivity of an CSCNT maybe reduced only about 6%.
[0043] Bundling is the term given to the mutual placement of CNTs
such that the tubes are maximally proximate or near maximally
proximate to each other. In the case of a MWNT, the nested shells
are intrinsically bundled. In the case of numerous MWNTs, bundling
is accomplished by placing the MWNTs in a maximally proximate
configuration. In the case of SWNTs, bundling is accomplished by
placing the SWNTs in a maximally proximate configuration.
Similarly, in the case of a mixture of SWNT(s) and MWNT(s),
bundling is accomplished by placing these CNTs in a maximally
proximate configuration.
SUMMARY OF THE INVENTION
[0044] The present invention provides a composition comprising a
single-walled or multi-walled carbon nanotube, having
phase-coherent or phase incoherent superconductivity above about 20
K.
[0045] The present invention provides a composition comprising a
multi-walled carbon nanotube, having phase-coherent
superconductivity above about 20 K.
[0046] The present invention provides a composition comprising a
bundle of single-walled or multi-walled carbon nanotubes, having
phase-coherent or phase incoherent superconductivity above about 20
K.
[0047] The present invention provides a composition comprising a
bundle of multi-walled carbon nanotubes, having phase-coherent
superconductivity above about 20 K.
[0048] The present invention provides a composition comprising a
matrix including bundles of multi-walled nanotubes, having
phase-coherent superconductivity above about 20 K.
[0049] the present invention provides a composition comprising a
matrix including bundles of single-walled nanotubes, having
phase-coherent superconductivity above about 20 K.
[0050] The present invention provides a composition comprising a
matrix including bundles of single-walled and multi-walled
nanotubes, having phase-coherent superconductivity above about 20
K.
[0051] The present invention also provides methods of achieving a
large positive magnetoresistance in bundles of superconducting
carbon nanotubes above about 20 K.
[0052] The present invention also provides superconducting quantum
interference devices comprising a composition of this
invention.
[0053] The present invention also provides magnetic reading heads
comprising a composition of this invention.
[0054] The present invention also provides magnetic switch devices
comprising a composition of this invention.
[0055] The present invention also provides magnetic image devices
comprising a composition of this invention.
[0056] The present invention also provides conductive elements
comprising a composition of this invention.
[0057] The present invention also provides two or more electronic
elements interconnected by a conductive element comprising a
composition of this invention.
[0058] The present invention also provides a method for forming
superconducting materials comprising forming a composition
including nanotubes or nanotube bundles of this invention, aligning
the nanotubes or bundles and forming the aligned nanotube or
bundles into an elongate form.
DESCRIPTION OF THE DRAWINGS
[0059] The invention can be better understood with reference to the
following detailed description together with the appended
illustrative drawings in which like elements are numbered the
same:
[0060] FIG. 1A depicts the temperature dependence of the remnant
magnetization for multi-walled nanotubes. After [1];
[0061] FIG. 1B depicts the field-cooled susceptibility as a
function of temperature in a field of 0.020 Oe. After [1];
[0062] FIG. 2 depicts the temperature dependence of the conductance
for a multi-walled nanotube rope (reproduced from Ref [3]);
[0063] FIG. 3A depicts the Hall coefficient versus temperature for
a nanotube rope (reproduced from Ref. [3]);
[0064] FIG. 3B depicts the Hall voltage as a function of magnetic
field measured at different temperatures, solid lines are drawn to
guide the eye (reproduced from Ref. [3]);
[0065] FIG. 4 depicts the Hall coefficient component for physically
separated tubes (PS) and the component for Josephson-coupled
superconducting tubes (JC);
[0066] FIG. 5A depicts the Hall voltage component for physically
separated tubes (PS) at 5 K;
[0067] FIG. 5B depicts the Hall voltage component for
Josephson-coupled superconducting tubes (JC) at 5 K;
[0068] FIG. 6A depicts the temperature dependence of the four-probe
resistance for a single MWNT with d=17 nm (reproduced from Ref
[20]);
[0069] FIG. 6B depicts the temperature dependence of the resistance
over 10-60 K, which is fitted by R(T)=R.sub.ct+aT.sup.P. The
fitting parameters: R.sub.ct=5.6(5)k.OMEGA., p=-0.65(9), and
a=29(4)k.OMEGA.K.sup.0.65;
[0070] FIG. 7A depicts the temperature dependence of the resistance
for a SWNT (data extracted from Ref. [26]);
[0071] FIG. 7B depicts the temperature dependence of the resistance
for three ultra-thin MoGe wires. The curves are smoothed from the
original plot of Ref. [18];
[0072] FIG. 8 depicts the I-V characteristic observed in a MWNT
with d=9.5 nm. The figure is reproduced from Ref. [30];
[0073] FIG. 9 depicts the critical current I.sub.c(T) for a SWNT
rope (data extracted from Ref. [38]), solid line represents
calculated curve using Eq. 8 and T.sub.c0=580 mK;
[0074] FIG. 10A depicts the critical currents i.sub.c's at 300 K
for the individual superconducting layers in a MWNT with d=9.5 nm
and in a MWNT with d=15 nm (data extracted from Ref. [30]);
[0075] FIG. 10B depicts the mean-field critical temperature,
I.sub.c's, of individual superconducting layers in the MWNTs with
d=9.5 nm and 15 nm, respectively, (T.sub.c0's are calculated using
Eq. 9 and assuming i.sub.c=i.sub.c1);
[0076] FIG. 11A depicts the temperature dependence of the frequency
for the Raman-active Big mode of a 90 K superconductor
YBa.sub.2Cu.sub.3O.sub.7-y (data extracted from Ref. [42]);
[0077] FIG. 11B depicts the difference of the measured frequency
and the linearly fitted curve above T.sub.c;
[0078] FIG. 12 depicts the temperature dependence of the frequency
for the Raman active G-band of single-walled carbon nanotubes
containing different concentrations of the magnetic impurity Ni:Co
(curves reproduced from the original plot of Ref. [41]);
[0079] FIGS. 13A, B & C depict the difference between the
measured frequency and the linearly fitted curve above the kink
temperatures (see text);
[0080] FIG. 14 depicts the T.sub.c0 as a function of the magnetic
impurity (Ni:Co) concentration in SWNTs;
[0081] FIG. 15A depicts the resistance data as a function of
T/T.sub.c0 for the smallest diameter SWNT with d=0.42 nm (data
extracted from Ref. [46]);
[0082] FIG. 15B depicts the temperature dependence of the
resistance below 0.5T.sub.c0 (data are well fitted by
R(T)=R.sub.o+T.sub..beta. with .beta.=1.77.+-.0.18;
[0083] FIG. 16 depicts temperature dependence of the resistivity
for a SWNT rope (data extracted from Ref. [47]);
[0084] FIG. 17 depicts temperature dependence of the resistance for
a single-walled nanotube with d=1.5 nm (data extracted from Ref.
[49]);
[0085] FIG. 18 depicts the calculated T.sub.c as a function of the
areal carrier density for InSb wires of the cross sections of 50
nm.times.10 nm and 80 nm.times.10 nm (curves reproduced from the
original plot of Ref [55]);
[0086] FIG. 19 is an illustration of the decrease in resistance
with the increase in the number of the conducting layers in the
MWNTs, where R is resistance;
[0087] FIG. 20 is an illustration of the effect the SWNT bundles
have on resistance, where diameters of the SWNTs in the bundle are
not necessarily identical and R is resistance;
[0088] FIG. 21 is an illustration of the effect MWNT bundle
configuration has on resistance, where the diameters and the
numbers of the adjacent superconducting layers of the MWNTs in the
bundle are not necessarily identical and R is resistance; and
[0089] FIG. 22 is an illustration of superconducting quantum
interference devices (SQUIDs) constructing from two phase coherent
superconducting MWNTs or from two phase coherent superconducting
bundles.
DETAILED DESCRIPTION OF THE INVENTION
[0090] The inventor has found that certain chiral carbon nanotubes
display superconducting properties at or above room temperature.
Although the inventor has found that any carbon nanotubes can be
made into superconductors through judicious doping, chiral
nanotubes having metallic chiralities are preferred. Carbon
nanotubes can be electron doped or hole doped. Doping can be
achieved via gate charging, interfacing with a metal having a
different work function from the tube, or a chemical or a physical
dopant selected from the group consisting of oxidants, reductants,
dopants resulting from atom or ion implantation, dopants from
charged particle bombardment or the like. The preferred doping
method is the gate charging where doping does not introduce
disorder. Metallic chirality carbon nanotubes are capable of
superconducting with even minor amount of doping and can
superconduct at any doping level in excess of a threshold dopant
level. For example, SWNTs with metallic chiralities and a diameter
of d=1.5 nm exhibit phase incoherent superconductivity above 600 K
when the doping lever is about 0.3% per carbon. The preferred
doping level corresponds to a Fermi level such that the first
metallic subband is nearly occupied. The relationship between the
Fermi energy E.sub.F and carrier concentration per carbon n is
given by n=0.0204.vertline.E.sub.F.vertline./d, where the diameter
d is in unit of nanometer and the Fermi energy E.sub.F is in unit
of eV. When the concentration of doped holes or electrons is close
to 0.019/d.sup.2 per carbon, the first subband is completely
occupied. The preferred diameter of the tube for maximizing
superconducting transition temperature is about 1 nm.
[0091] The inventor has also found a composition and method of
obtaining phase-coherent or nearly phase-coherent high temperature
superconductivity whereby nested metallic chirality layers in MWNT
are formed whereby the resistance can be tuned based on the number
of nested metallic chirality layers--an increase in layers
decreases resistivity. The most phase coherent superconductivity
occurs when all the nested layers have metallic chiralities and the
intra-nested tube distance is as small as possible. This is due to
an effective increase in the number of the transverse channels via
the Josephson coupling of adjacent superconducting layers. The
resistance decreases exponentially with increasing nested
superconducting layers. The zero resistance or phase coherent state
can be approached in a single MWNT that consists of nested
superconducting layers that meet or surpass the minimum number of
nested layers to achieve high temperature superconductivity.
[0092] The inventor has also found a composition and method of
obtaining phase-coherent or nearly phase-coherent high temperature
superconductivity. SWNTs are bundled by putting several metallic
chirality SWNTs in parallel and packed adjacent to each other. This
results in a much lower resistance than the sum of the individual
tubes. The diameters of the SWNTs in the bundle are not necessarily
identical. The preferred embodiment occurs where the inter-tube
distance is as close as possible. The Josephson coupling among the
tubes can suppress the QPS and lower the resistance
exponentially.
[0093] The inventor has also found a composition and method of
obtaining phase-coherent or nearly phase-coherent high temperature
superconductivity whereby several phase-incoherent superconducting
MWNTs are put in parallel and packaged in an adjacent
configuration, the resulting bundle has lower resistance than the
sum of the individual tubes. The diameters and the numbers of the
adjacent superconducting layers of the MWNTs are independent and
need not be identical. The preferred embodiment occurs where the
inter-tube distance is as close as possible. The Josephson coupling
among the tubes can suppress the QPS thereby exponentially lowering
the resistance and approaching the zero resistance state.
[0094] The inventor has also found a composition and method of
obtaining phase-coherent or nearly phase-coherent high temperature
superconductivity whereby several phase-incoherent superconducting
MWNTs and SWNTs are put in parallel and packaged in an adjacent
configuration, the resulting bundle has lower resistance than the
sum of the individual tubes. The preferred embodiment occurs where
the inter-tube distance is as close as possible.
[0095] The inventor has also found a composition and method of
obtaining phase-coherent or nearly phase-coherent high temperature
superconductivity by combining the embodiments above whereby a
bundle of MWNTs and SWNTs are combined.
[0096] As discussed above, phase coherent superconducting materials
can be constructed by forming aggregates of superconducting carbon
nanotubes (SCNTs) where the nanotubes are in proximity to each
other in an aligned orientation, preferably in maximal proximity.
The condition where a considerable portion of lengths of two or
more nanotubes are aligned along an axis and are in close
proximity, preferably maximal proximity, and are wrapped into
bundles with a spiral winding--or otherwise--to maintain the
alignment and intimate proximity or to control the alignment and
proximity or to vary the alignment and proximity should prove to
secure electronic properties of the collection of SCNTs. A
preferred implementation is the securing in a maximally proximate
manner of optimally doped superconducting MWNTs-optimized in terms
of the doping and chirality.
[0097] The inventor has also found that there is a very large
positive magnetoresistance (MR) effect in bundles of
superconducting carbon nanotubes. The bundles are preferably
closely packed, as discussed above. In order to have a substantial
low field MR effect, the size of superconducting bundles must
exceed a critical value. The critical value of the size is
inversely proportional to the square root of the magnetic field
used in the application. Any existing device in which materials
with this type MR effect are used can be converted into new devices
where the old materials are replaced by bundles of superconducting
carbon nanotubes of this invention. The new devices will have
improved performances.
[0098] The inventor has also found that very sensitive magnetic
reading heads can be constructed from bundles of superconducting
carbon nanotubes, which have a large MR effect. A magnetic field
created from a ferromagnetic domain in a tape or a diskette changes
the resistance of the reading head comprising a bundle of
superconducting carbon nanotubes. Because of the very large MR
effect, any small change in the magnetic field can lead to a large
change in the resistance of the head. Therefore, the sensitivity of
the magnetic reading head will be very high. Moreover, the size of
the head can be very small (on the order of 50 nm), so the spatial
resolution is also very high. The performance of this type of
magnetic reading heads should be superior to any one in the
market.
[0099] The inventor has also found that because of the superior
sensitivity and spatial resolution, the magnetic reading head can
be used as a sensor of high resolution magnetic imaging
spectroscopy. With this spectroscopy, the magnetic domain patterns
in magnetic materials can be clearly seen. This spectroscopy will
be a powerful device to diagnose magnetic memory cards, magnetic
taps and diskettes, current distributions of chips, and so on.
[0100] The inventor has also found that very sensitive magnetic
switch devices can be constructed from bundles of superconducting
carbon nanotubes, which have a large MR effect. A small change of
the magnetic fields near a bundle of superconducting carbon
nanotubes will lead to a large change in the resistance of the
bundle. The magnetic field can be produced by a current or a
permanent magnet. Changing the current or the distance between the
permanent magnet and the bundle gives rise to the change in the
magnetic field near the bundle and therefore to the change of the
resistance in the bundle. The change of the resistance in the
bundle serves as an input signal to trigger an electrical switch to
open or close.
[0101] The inventor has also found that superconducting quantum
interference devices (SQUIDs) can be constructed from
phase-coherent superconducting nanotubes. A single phase-coherent
MWNT is preferred for this type of device. This device can probe an
extremely weak magnetic field, operate at room temperature, and
have a superior spatial resolution. This superior performance of
the device enables it to map the magnetic field distribution in the
body of our human being, which is closely related to our health.
Therefore it can be used to diagnose our symptoms, leading to an
important application in medicine. The room temperature SQUIDs
should have much broader applications than conventional low
temperature SQUIDs.
[0102] The inventor has also found that superconducting materials
can be prepared from multi-layered graphite or graphene sheets that
are appropriately doped. Preferably, the graphite or graphene
materials comprise graphite sheets that have the same structure.
Such structures, when appropriately doped, will superconduct,
coherently or incoherently, at temperatures above 100 K, preferably
above about 200 K and particularly at or above about 300 K.
[0103] Transport and Magnetic Properties in Multi-wall Carbon
Nanotube Ropes: Evidence for Superconductivity above Room
Temperature
[0104] Here, the inventor provides detailed data analyses on the
existing data for multi-walled nanotube ropes. In terms of the
coexistence of physically separated (PS) tubes and
Josephson-coupled (JC) superconducting tubes with superconductivity
above room temperature, the inventor can consistently explain the
temperature dependencies of the Hall coefficient, the
magnetoresistance effect, the remnant magnetization, the
diamagnetic susceptibility, and the conductance, as well as the
field dependence of the Hall voltage. The inventor also interprets
the observed paramagnetic signal and unusual field dependence of
the magnetization at 300 K as arising from the paramagnetic
Meissner effect in a multiply connected superconducting
network.
[0105] The inventor first discusses the temperature dependencies of
the remnant magnetization M.sub.r and the diamagnetic
susceptibility for his mult-walled nanotube ropes. Plotted in FIG.
1 are the experimental results which are reproduced from Ref. 1. It
is apparent that the temperature dependence of the M.sub.r (FIG.
1A) is similar to that of the diamagnetic susceptibility (FIG. 1B)
except for the opposite signs. This behavior is expected for a
superconductor. The M.sub.r was also observed by Tsebro et al. up
to 300 K [2]. However, the observation of the M.sub.r alone does
not give evidence for superconductivity since the M.sub.r could be
caused by ferromagnetic impurities and/or ballistic transport.
[0106] The inventor can rule out the existence of ferromagnetic
impurities. If there were ferromagnetic impurities, the total
susceptibility would tend to turn up below 120 K where the M.sub.r
increases suddenly. This is because the paramagnetic susceptibility
contributed from the ferromagnetic impurities would increase below
120 K. In contrast, the susceptibility suddenly turns down rather
than turns up below 120 K (FIG. 1B). This provides strong evidence
that the observed M.sub.r in the nanotubes has nothing to do with
the presence of ferromagnetic impurities.
[0107] FIG. 2 shows temperature dependence of the conductance for a
multi-walled nanotube rope, which is reproduced from Ref. 3. The
inventor has checked that the temperature dependence of the
conductance in his nanotube ropes is nearly the same as that shown
in FIG. 2. It is apparent that the conductance for the MWNT sample
tends to increase below 120 K at which both remnant magnetization
and the field-cooled diamagnetic signal suddenly increase. This
suggests that the magnetic properties are closely related to the
electrical transport of the nanotubes.
[0108] Alternatively, the increase of the conductance below 120 K
could be due to the increase in the ballistic conduction channels
(perfect conductivity). However, this scenario cannot consistently
account for the observed increase of the field-cooled diamagnetic
signal below 120 K since perfect conductors cannot expel the
magnetic flux in the field-cooled condition.
[0109] In FIG. 3, the inventor shows the temperature dependence of
the Hall coefficient (FIG. 3A) and the field dependence of the Hall
voltage (FIG. 3B) for a multi-walled nanotube rope. The figures are
reproduced from Ref. 3. It is striking that the Hall coefficient
increases rapidly below about 120 K at which all three quantities
in FIG. 1 and FIG. 2 increase suddenly. The fact that such a strong
temperature dependence below 120 K was not seen in physically
separated tubes [4] suggests that this is not an intrinsic property
of a single tube, but associated with the coupling of the tubes.
Below the inventor will interpret these data in a consistent way by
considering the coexistence of physically separated (PS) tubes and
Josephson-coupled (JC) superconducting tubes with superconductivity
above room temperature.
[0110] It is well known that the carbon nanotubes have two types of
electronic structure depending on the chirality [5, 6], which is
indexed by a chiral vector (n,m): n-m=3N+.nu., where N, n, m are
the integers, and .nu.=0, +i. The tubes with .nu.=0 are metallic
while the tubes with .nu.=+1 are semiconductive. The multi-walled
nanotubes consist of at least two concentric shells which could
have different chiralities. Presumably, each shell should exhibit
phase incoherent superconductivity when it is sufficiently doped.
If there are sufficient adjacent superconducting shells that are
Josephson coupled, a single MWNT could become a phase coherent
non-dissipative superconductor. If phase incoherent superconducting
tubes are closely packed into a bundle, the bundle could become a
phase coherent superconductor via Josephson coupling. It is also
possible that some tubes are not superconducting due to
insufficient doping.
[0111] The inventor could classify the tubes in a rope into
physically separated (PS) tubes and Josephson-coupled (JC)
superconducting tubes with superconductivity above room
temperature. Since the properties for physically coupled
nonsuperconducting tubes should have no differences from that for
physically separated nonsuperconducting tubes, The inventor
considers all nonsuperconducting tubes as physically separated
tubes.
[0112] The Hall coefficient for physically separated tubes should
be positive, as reported in Ref. [4]. The Hall coefficient for a
single non-dissipative superconducting MWNT should be zero because
no vortices could be trapped into the single tube whose dimension
should be much smaller than the inter-vortex distance. The
physically separated nonsuperconducting and phase-incoherent
dissipative superconducting tubes should have a positive Hall
coefficient similar to that in the normal state. On the other hand,
vortices can be trapped into Josephson-coupled superconducting
tubes, leading to a vortex-liquid state above a characteristic
field that depends on the Josephson coupling strength. As seen in
both cuprates and MgB.sub.2 [7, 8], the low-field Hall coefficient
RH in the vortex-liquid state is negative below T.sub.c, reaching a
minimum at T.sub.k, and then increasing towards zero with further
decreasing temperature. Below the characteristic temperature
T.sub.k, vortices start to be pinned so that magnitudes of the Hall
conductivity, longitudinal conductivity, the critical current
(remnant magnetization), and diamagnetic susceptibility increase
simultaneously. This can naturally explain why the conductance, the
diamagnetic susceptibility, the remnant magnetization, and the Hall
coefficient simultaneously increase below about 120 K, as seen from
FIG. 1, FIG. 2 and FIG. 3A.
[0113] The inventor can decompose the total Hall coefficient into
two components: one is for Josephson-coupled superconducting tubes
(JC) and another for physically separated tubes (PS). The PS
component is proportional to the measured Hall coefficient for
physically separated tubes [4] with the constraint that, at zero
temperature, the magnitude of the PS component is equal to the
total Hall coefficient. The JC component is obtained by subtracting
the total Hall coefficient from the PS component. FIG. 4 shows both
PS (dashed line) and JC (solid line) components. It is apparent
that the JC component has a local minimum at T.sub.k=120 K. The
negative value of the JC component remains up to 200 K. This
suggests that the superconducting transition temperature is far
above 200 K.
[0114] Similarly, as seen in cuprates and MgB.sub.2 [7, 8, 9], the
Hall voltage V.sub.H in the vortex-liquid state is negative,
passing through a minimum at B.sub.k, and then increasing towards
the normal-state value with further increasing temperature. Below
B.sub.k, V.sub.H tends to zero. Interestingly, both B.sub.o and
B.sub.k can be independently obtained from the field dependence of
the longitudinal resistivity, as described in Ref. 9.
[0115] The inventor can also decompose the total Hall voltage into
two components: one for Josephson-coupled superconducting tubes
(JC) and another for physically separated tubes (PS). Plotted in
FIG. 5A is the PS component at 5 K, which is proportional to the
measured Hall voltage for physically separated tubes [4] and
matches with the low field data shown in FIG. 3B. FIG. 5B shows the
JC component at 5 K, which is obtained by subtracting the total
Hall voltage from the PS component. The decomposition was performed
after the data in FIG. 3B were smoothed. The inventor can see that
the field dependence of the JC component is quite similar to that
for cuprates and MgB.sub.2 [7, 8, 9] except that B.sub.o in the
MWNTs is rather small, which may be due to a weak pinning
potential. FIG. 5B also indicates that the magnitude of B.sub.k is
larger than 5 T, in agreement with the longitudinal
magnetoresistance data (see below).
[0116] The longitudinal magnetoresistance at 300 K mainly arises
from the Josephson-coupled superconducting tubes since the
contribution from the physically separated tubes is negligible [4].
From the magnetoresistance data at 300 K [3] and the criterion for
determining B.sub.k[9], the inventor finds that B.sub.k.apprxeq.3.0
T at 300 K. Using the relation
B.sub.k(T)=B.sub.k(0)(1-T/T.sub.c).sup.1.5 [9], T.sub.c=650 K [1],
and B.sub.k(300 K)=3.0 T, one has B.sub.k(5 K)=7.5 T. This could
explain why one has not seen the local minimum in V.sub.H below 5
T. It is highly desirable to perform the Hall effect experiment up
to 15 T to see the crossover field B.sub.k.
[0117] Within this two component model, the inventor can also
explain the unusual magnetoresistance (MR) effect below 150 K.
Because the physically separated tubes produce a negative MR effect
at low temperatures while the Josephson-coupled superconducting
tubes generate a positive MR effect, the opposite contributions
from the two components can lead to a local minimum at certain
magnetic field. This is indeed the case (see FIG. 1 of Ref. 3). At
high temperatures, the negative MR effect contributed from the
physically separated tubes becomes weak so that the positive MR
effect is mainly contributed from the Josephson-coupled
superconducting tubes, in agreement with the experimental results
[1, 3].
[0118] There are more experimental results that support the thesis
of room temperature superconductivity in multi-walled nanotubes.
The observation of the paramagnetic signal at 300 K below H=2 kOe
[10] is remarkable, which can be explained as arising from the
presence of ferromagnetic impurities or from the paramagnetic
Meissner effect below the superconducting transition temperature,
as observed in ceramic cuprate superconductors [11] and in
multijunction loops of conventional superconductors [12]. For
H=4000e, the temperature dependence of the susceptibility for the
nanotube sample (see FIG. 8 of Ref. 10) is similar to that for a
ceramic cuprate superconductor in a low field (see FIG. 10a of Ref.
11). The M (H) curve below H=10 kOe (see FIG. 7 of Ref. 10) can be
compatible with the presence of ferromagnetic impurities. However,
such ferromagnetic impurities should be detectable in the
high-field magnetization curve by an intercept in the extrapolation
for H.fwdarw.0. The intercept was found to be nearly zero at 300 K
in the samples of Ref. 10. In the inventor's samples prepared from
graphite rods with the same purity (99.9995%), the intercepts are
negligible in the whole temperature range of 250 K to 400 K. For
less pure C.sub.60 and graphite samples, the contamination of
ferromagnetic impurities is clearly seen from the M (H) curve in
the high-field range [10]. The clear "ferromagnetic" signal
observed only in the low field range [10] is similar to the case in
granular superconductors [11]. The "ferromagnetic" signal may be
caused by a "ferromagnetic" ordering of elementary long-thin
current loops [13]. The critical magnetic field below which the
"ferromagnetic" state is stable should depend on the number of
filaments per current loop. The large critical field of about 10
kOe in the samples of Ref. 10 suggests that a current loop may
correspond to a bundle consisting of a large number of tubes.
[0119] Quasi-one-dimensional Superconductivity above 300 K and
Quantum Phase Slips in Individual Carbon Nanotubes
[0120] Here the inventor extensively analyzes a great amount of the
existing data for electrical transport, the Altshuler Aronov Spivak
and Aharonov Bohm effects, as well as the tunneling spectra of
individual carbon nanotubes. The data can be explained by theories
of the quantum phase slips in quasi-one-dimensional
superconductors. The existing data consistently suggest that the
mean-field superconducting transition temperature T.sub.c0 in both
single-walled and multi-walled carbon nanotubes could be higher
than 600 K. Remarkably, the QPS theories can naturally explain why
the resistances in the closely packed nanotube bundles or in the
individual multi-walled nanotubes with large diameters approach
zero at room temperature, while a single tube with a small diameter
has a non-zero resistance.
[0121] It is known that superconducting fluctuations in
one-dimensional (1 D) superconductors play an essential role in the
resistive transition. Slightly below superconducting transition
temperature T.sub.c0, 1D superconductors have a finite resistance
due to thermally activated phase slips (TAPS) [14]. A number of
experiments have also demonstrated a large resistance well below
T.sub.c0 in thin superconducting wires [15, 16, 17, 18]. Further, a
crossover to an insulating state has been observed in ultra-thin
PbIn wires with diameters of the order of 10 nm [15, 17] as well as
in ultra-thin wires of MoGe [18].
[0122] Theories based on the quantum phase slips can explain the
finite resistance in 1D superconductors [16, 19]. Essentially, the
phase slips at low temperatures are related to the macroscopic
quantum tunneling (MQT), which allows the phase of the
superconducting order parameter to fluctuate between zero and 2.pi.
at some points along the wire, resulting in voltage pulses. The QPS
tunneling rate is proportional to exp (-S.sub.QPS), where S.sub.QPS
in clean superconductors is very close to the number of transverse
channels N.sub.ch in the limit of weak damping (see below). If the
number of the transverse channels N.sub.ch is small, the QPS
tunneling rate is not negligible, leading to a non-zero resistance
at low temperatures. For a single-walled nanotube (SWNT),
N.sub.ch=2, implying a large QPS tunneling rate and thus a large
resistance even if it is a superconductor. For MWNTs with several
superconducting layers adjacent to each other, the number of the
transverse channels will increase substantially, resulting in the
suppression of the QPS. If two superconducting tubes are closely
packed together to effectively increase the number of the channels,
one would find a small resistance at room temperature if the
constituent tubes have a mean-field T.sub.c0 well above room
temperature. This can naturally explain why a single MWNT with a
diameter d of about 17 nm has a finite on-tube resistance at room
temperature [20, 21] while a bundle consisting of two tubes has a
negligible on-tube resistance [22].
[0123] There are thermally activated phase slips and quantum phase
slips in a thin superconducting wire. In a theory developed by
Langer, Ambegaokar, McCumber and Halperin [14], such phase slips
occur via thermal activation. The resistance due to the TAPS is
given by [23] 1 R T A = ( h 4 e 2 ) ( k B T ) exp ( - F 0 k B T ) (
1 )
[0124] where the attempt frequency .OMEGA. is given by [14] 2 = ( 3
1 2 2 3 2 ) ( L ) ( F 0 k B T ) 1 2 ( 1 ) ( 2 )
[0125] where L is the length of the wire, 4 is the coherence
length, and h/.tau.=(8/.pi.)k.sub.B(T.sub.c-Y). The barrier energy
.DELTA.F.sub.o is 3 F 0 = ( 2 7 2 3 ) ( H c 2 8 ) A ( 3 )
[0126] where H.sub.c.sup.2/8.pi. is the condensation energy and A
is the cross-section area of the wire. The condensation energy is
equal to N (0).DELTA..sup.2/2 within the BCS theory, where N(0) is
the average density of states near the Fermi level over the energy
scale of the superconducting gap .DELTA.. For a metallic SWNT with
N.sub.Ch=2, N (0).DELTA.=4/(3.pi.a.sub.c-cy.sub.o) (Ref. 24),
.nu..sub.F=1.5a.sub.c-c.g- amma..sub.o (Ref 25), where
.gamma..sub.o is the hopping integral, r is the radius of the tube,
and .sub.c-c is the bonding length. Using
.xi.=.nu..sub.F/.pi..DELTA. and the above relations, one can
readily show that .DELTA.F.sub.o.tau./=0.13 N.sub.ch and
.DELTA.F.sub.o.congruent.0.19 N.sub.ch. For MWNTs with N.sub.m
metallic layers, .DELTA.F.sub.o.tau.=0.2- 6 N.sub.m and
.DELTA.F.sub.o/.DELTA.=0.38 N.sub.m.
[0127] It was shown that the TAPS is significant only at
temperatures very close to and below T.sub.c0 [14]. At lower
temperatures, the finite resistance is caused by MQT and is given
by [16], 4 R MQT = 1 ( h 4 e 2 ) ( L ) ( 2 F 0 ) 1 2 exp ( - 2 F 0
/ ) ( 4 )
[0128] where .beta..sub.1 and .beta..sub.2 are constants, depending
on the damping strength. When the damping increases, .beta..sub.2
decreases. Substituting .DELTA.R.sub.o.tau./=0.26N.sub.m into Eq.
4, the inventor finds that 5 R MQT = 1 ( h 4 e 2 ) ( L ) ( 0.26 2 N
m ) 1 2 exp ( - 0.26 2 N m ) ( 5 )
[0129] From Eq. 5, one can see that S.sub.QPS=2N.sub.m in the limit
of weak damping where .beta..sub.2=7.2 (Ref. 16). For a stronger
damping, P2 is reduced so that S.sub.QPS<2N.sub.m. Moreover, in
the dirty limit, S.sub.QPS will be further reduced [19] such that
S.sub.QPS<<2N.sub.- m. For a SWNT, N.sub.m=1 so that a large
QPS and a nonzero resistance is expected below the mean-field
superconducting transition temperature. If several superconducting
SWNTs are closely packed to ensure an increase in the number of
channels, the QPS would be substantially reduced. This can explain
why the resistance is finite at room temperature for a single SWNT
[26, 27] while the resistance at room temperature is very small for
a bundle consisting of two strongly coupled SWNTs [21]. For a MWNT
with d=40 nm, there is a total of 27 metallic layers, that is,
N.sub.m=27 (Ref. 28). This implies that the QPS in this single MWNT
should be strongly suppressed according to Eq. 5. Indeed, this MWNT
has nearly zero resistance at room temperature over a length of 4
.mu.m (Ref. 28).
[0130] A more rigorous approach to the QPS in quasi-1D
superconductors [19] suggests that S.sub.QPS depends not only on
the quantity .DELTA.F.sub.o.tau./ but also on the normal-state
conductivity .sigma.(S.sub.QPS.varies..sigma..sup.2/3) Therefore,
one can very effectively suppress the QPS and the resistance below
T.sub.c0 by reducing the normal-state resistivity. It was shown
that the electron backscattering from single impurity with long
range potential is nearly absent in metallic SWNTs while this
backscattering becomes significant for doped semiconducting SWNTs
[29]. This implies that the QPS in doped metallic SWNTs will be
significantly smaller than that in doped semiconducting SWNTs if
both systems become superconducting by doping.
[0131] Now the inventor discusses the temperature dependence of the
resistance observed in nanotubes. FIG. 6A shows the temperature
dependence of the four-probe resistance for a single MWNT with d=17
nm, which is reproduced from Ref. 20. It is remarkable that the
resistance increases with decreasing temperature, but saturates at
low temperatures. This unusual temperature dependence is very
difficult to be explained consistently in terms of the conventional
theory of transport [20]. However, a theory based on the QPS in 1 D
superconductors can naturally explain this unusual behavior. It was
shown that [19], the resistance R.about.T.sup.2.UPSILON.-3 for
k.sub.BT>>.PHI..sub.oI/c, and R becomes independent of
temperature and is proportional to I.sup.2.mu.-3 for
k.sub.BT<<.PHI..sub.oI/c, where .PHI..sub.o is the quantum
flux, c is the speed of light, and I is the current. When
.mu.<1.5, R increases with decreasing temperature
(semiconducting behavior), while .mu.>1.5, R decreases with
decreasing temperature (metallic behavior). Only if the QPS are
strongly suppressed, zero or negligible resistance state can be
realized below T.sub.c0.
[0132] Based on the QPS theory, the inventor can readily show that,
for .PHI..sub.oI/ck.sub.B<<T<<T.sub.c, the four-probe
resistance R(T) is
R(T)=R.sub.ct+aT.sub.P (6)
[0133] where R.sub.ct is the tunneling resistance and p=2.mu.-3.
The tunneling resistance is given by R.sub.ct=R.sub.Q/tN.sub.ch,
where t is the transmission coefficient (t<1) and
R.sub.Q=h/2e.sup.2=12.9 k.OMEGA. is the resistance quantum.
[0134] In FIG. 6B, the inventor fit the resistance of the MWNT by
Eq. 6. The best fit gives R.sub.ct=5.6(5) k.OMEGA., p=-0.65(9), and
.alpha.=29(4) k.OMEGA. K.sup.0.65. The value of R.sub.ct suggests
that the intrinsic saturation resistance of the tube is 9.7
k.OMEGA..
[0135] From the value of R.sub.ct for the MWNT, the inventor can
estimate the transmission coefficient t. As discussed below, the
high bias transport measurements in MWNTs [30] suggest that there
is a total of 14 conducting layers in a MWNT with d=14 nm, and that
the number of the conducting layers is nearly proportional to d.
Then, the MWNT with d=17 nm should have about 17 conducting layers.
Moreover, the beautiful experiment reported by de Pablo et al. [28]
indicates that each conducting layer contributes 1 transverse
channel to electrical transport. Therefore, one expects N.sub.ch=17
in this MWNT, leading to t=0.135. This suggests that the tunneling
is far from being ideal, which may arise from non-Ohmic contacts.
It should be mentioned that each layer should contribute 2 channels
if there were no interlayer coupling. However, it has been shown
that the interlayer coupling can significantly modify the
electronic states near the Fermi level, leading to the modulation
in the number of channels between 1 and 3 for each layer (the
average number of channels over an energy scale of 0.1 eV remains 2
for each layer) [31, 32].
[0136] In FIG. 7A, the inventor plots the temperature dependence of
the resistance for a single SWNT. The data are extracted from Ref.
26. It is interesting that the temperature dependence of the
resistance in the single-walled nanotube is similar to that found
for ultra-thin wires of MoGe superconductors [18], which is
reproduced in FIG. 7B. The characteristic temperature T*
corresponding to the local resistance minimum depends on the
resistance in the normal state. It appears that T* decreases with
decreasing the resistance. The resistance at low temperatures could
be smaller or larger than that in the normal state. By comparing
FIG. 7A and FIG. 7B, one might infer that the mean-field T.sub.c0
of this nanotube is well above 270 K.
[0137] From the single-particle tunneling spectrum obtained through
two high-resistance contacts (see FIG. 6b of Ref. 27), the inventor
can clearly see a pseudo-gap feature appears at an energy of about
220 meV. The pseudo-gap feature should be related to the
superconducting gap. Considering the broadening of the gap feature
due to large QPS and the double tunneling junctions in series, The
inventor estimates the superconducting gap A to be about 100 meV.
The scanning tunnelling microscopy and spectroscopy [33] on
individual single-walled nanotubes also show the pseudo-gap
features with .DELTA.=100 meV in doped metallic SWNTs (E.sub.F is
about 0.2 eV below the top of the valence band). Using
k.sub.BT.sub.c0=.DELTA./1.76, one finds T.sub.c0=660 K. It is
interesting to note that the pseudo-gap feature could be explained
by Luttinger-liquid theory [34, 35] assuming that the Luttinger
parameter is far below the free fermionic value of 1. The fact that
the pseudo-gap feature is seen only in doped metallic chirality
tubes [33] but not in undoped armchair metallic chirality tubes
[36] may rule out the Luttinger-liquid explanation since
Luttinger-liquid behavior remains essentially unchanged with doping
[35].
[0138] Now the inventor explains one of the most remarkable
features observed in the carbon nanotubes. At large biases, the
current saturates at 19-23 .mu.A in SWNTs [27]. The current
saturation has been explained as due to the backscattering of the
zone-boundary optical phonons [27]. However, the deduced mean free
path for the phonon backscattering is one order of magnitude
smaller than the expected one from the tight-binding approximation
[27]. Further, the I-V characteristic observed in SWNTs is
temperature independent (Ref. 27) while the calculated I-V
characteristic within this mechanism strongly depends on
temperature especially in the low-bias range [37].
[0139] Alternatively, the inventor can explain the I-V
characteristics of both SWNTs and MWNTs [27, 30] in terms of
quasi-1D superconductivity. Essentially, the I-V characteristics of
both SWNTs and MWNTs [27, 30] are similar to that observed in
ultra-thin PbIn superconducting wires (see FIG. 8 of Ref. 17). FIG.
8 shows the I-V characteristic observed in a MWNT with d=9.5 nm.
The figure is reproduced from Ref. 30. When the applied current is
below I.sub.c1 the QPS are negligible so that the intrinsic on-tube
resistance is much smaller than the normal-state resistance, and V
depends on I quasi-linearly. The slope dV/dI is equal to the sum of
the on-tube resistance and the contact resistance. When the applied
current increases slightly above I.sub.c1, the on-tube resistance
rises rapidly towards the normal-state value due to large QPS,
leading to large dissipation that would burn the tube. If the tube
is not burned, the current tends to be saturated before the tube is
completely driven into the normal state. The saturation current is
close to the mean-field critical current I.sub.c in the absence of
defects. Since the phase slips occur initially near normal regions
located around defects in the sample, one expects that I.sub.c1
should strongly depend on the density of defects and thus on the
normal-state resistivity. From FIG. 8, one can see that
I.sub.c1<0.75I.sub.c.
[0140] According to the BCS theory, the mean-field critical current
in the clean limit is given by 6 I c ( T ) = n s ( T ) A [ ( T ) k
F ] ( 7 )
[0141] The superfluid density
n.sub.s(T)=n.lambda..sup.2(0)/.lambda..sup.2- (T), and the
normal-state carrier density n=2N(0)E.sub.F=2N(0).nu..sub.Fk.-
sub.F=4k.sub.F/A.pi.. Here one has used the relations:
N(0)A=4/(3.pi.a.sub.c-c.gamma..sub.o), and
.nu..sub.F=15a.sub.c-c.gamma..- sub.o, as well as
E=.nu..sub.F.vertline.k.vertline.. Substituting the above relations
into Eq. 7 yields 7 I c ( T ) = 7.04 N m ( k B T c0 e R Q ) [ 2 ( 0
) 2 ( T ) ] [ ( T ) ( 0 ) ] ( 8 )
[0142] with I.sub.c(0)=7.04N.sub.mk.sub.BT.sub.c0/eR.sub.Q. Here
.lambda..sup.2(0)/.lambda..sup.2(T) follows the BCS prediction, and
.DELTA.(T)=.DELTA.(0) tan h.sup.-1 [1.6(T.sub.c0/T-1).sub.1/2],
which is very close to that predicted by the BCS theory. The
critical current i.sub.c per superconducting layer is then given by
8 i c ( T ) = 7.04 N m ( k B T c0 e R Q ) [ 2 ( 0 ) 2 ( T ) ] [ ( T
) ( 0 ) ] ( 8 )
[0143] For a SWNT rope, the resistance starts to drop below about
550 mK and reaches a value R.sub.r=74 .OMEGA. at low temperatures
[38]. The data are consistent with quasi-1D superconductivity with
T.sub.c0=550 mK and N.sub.m=R.sub.Q/2R.sub.r=87 (Ref 38).
Substituting these numbers into the expression: I.sub.c(0)=7.04
N.sub.mk.sub.BT.sub.c0/eR.sub.Q, one obtains I.sub.c(0)=2.25 .mu.A,
in excellent agreement with the measured I.sub.c(0)=2.41 .mu.A, as
seen from FIG. 9. The solid line in FIG. 4 is the calculated curve
using Eq. 8 and T.sub.c0=580 mK. It is striking that the data are
in quantitative agreement with theory. It should be mentioned that
very low superconductivity in the SWNT rope may be due to the fact
that the tubes are very lightly doped. The very high normal-state
resistance (830 k.OMEGA./.mu.m) per tube [38] suggests that the
Fermi level must be very close to the top of the valence band where
the Fermi velocity must be significantly reduced due to the opening
of a small gap in non-armchair metallic tubes.
[0144] In FIG. 10A, the inventor shows the critical currents
i.sub.c1's at 300 K for individual superconducting layers in a MWNT
with d=9.5 nm and in a MWNT with d=15 nm. The data are extracted
from Ref. 30. The layer number starts from 0 that corresponds to
the outermost superconducting layer. For d=9.5 nm the i.sub.c tends
to decrease with decreasing the diameter of the layer, while for
d=15 nm the tendency is just opposite. Plotted in FIG. 10B is the
mean-field critical temperature T.sub.c0's of individual
superconducting layers in the MWNTs, which are calculated using Eq.
9 and assuming i.sub.c=i.sub.c1. It is clear that the calculated
T.sub.c0's are underestimated because i.sub.c is always larger than
i.sub.c1, as seen in FIG. 8. One can see that T.sub.c0 varies from
430 K to 610 K, in good agreement with the independent resistance
data [10]. The broad variation in T.sub.c0 suggests that T.sub.c0
depends on doping and the diameters of tubes.
[0145] Now the inventor turns to discuss the Aharonov Bohm (AB)
effect, which has been observed in MWNTs when the magnetic field is
applied along the tube-axis direction [39, 20]. The
magnetoresistance measurements showed pronounced resistance
oscillations as a function of magnetic flux. The oscillation period
was found to be about .PHI..sub.o (=hc/2e) if one assumed that only
the outermost layer is involved in conduction [39, 20]. The result
could be consistent with the Altshuler Aronov Spivak (AAS) effect,
which arises from quantum interference of two counter-propagating
closed diffusive electron trajectories. On the other hand, a period
of 2.PHI..sub.o should have been observed if the phase coherence
length of single particles is reasonably larger than .pi.d (the AB
effect for the single particle density of states [40]). If the
phase coherence length L.phi. deduced from experiment (e.g.,
L.phi..about.300 nm>>.pi.d in one of the MWNTs [39]) were
related to that for single particles, one would have observed the
AB effect. However, such an effect has never been observed [39,
20]. Therefore, this contradiction cannot be resolved if the
conduction carriers were single particles.
[0146] The inventor can resolve the above discrepancy if the
inventor assumes that the conduction carriers are Cooper pairs in
the limit of weak localization (WL). It was argued that the
uncertainty in the phase of Cooper pairs due to the large QPS could
lead to weak localization of the Cooper pairs [18]. In many
situations, a Cooper pair can be equivalent to a particle with a
charge of 8. Therefore, the WL theory for single particles should
be applicable for Cooper pairs upon replacing e with 2e. With this
simplification, one can readily find that the magnetic-flux period
of the AAS effect for the Cooper pairs is .PHI..sub.o/2, and that
the AB effect for the single particle density of states should be
absent if the phase coherence length for single particles is less
than .pi.d.
[0147] In fact, the assumption that only the outermost layer is
conducting [20, 39] is not justified. As the inventor discussed
above, 14 and 27 layers are involved in conduction in MWNTs with
d=14 nm and 40 nm, respectively. Further, the resistance at 1.3 K
for a MWNT with d=13 nm is 2.45 k.OMEGA. (Ref. 39). The value of
the resistance suggests that there are at least 6 transverse
channels and 6 conducting layers are involved in conduction. The
average magnetic flux sensed by the carriers in all the conducting
layers should be B.pi. (r.sub.out.sup.2+r.sub.in.sup.2)/2, where
r.sub.out, and r.sub.in are the radii of the outermost and
innermost conducting layers, respectively, and B is the magnetic
field. One can calculate r.sub.in using the relation
r.sub.in=r.sub.out-0.34 (N.sub.m-1) nm. For the MWNT with d=17 nm,
N.sub.m=17 (see above), leading to r.sub.in=3.06 .mu.m. From the
measured magnetic-field period of 8.2 Tin the MWNT [20], one finds
that the magnetic-flux period is 0.51 .PHI..sub.o, in quantitative
agreement with the thesis that the charge carriers are Cooper pairs
with a finite phase coherence length due to the QPS.
[0148] Raman Spectroscopic Evidence for Superconductivity at 645 K
in Single-wall Carbon Nanotubes
[0149] Here the inventor analyzes the data of the temperature
dependent frequency shifts of the Raman active G-band in
single-walled carbon nanotubes containing different concentrations
of the magnetic impurity Ni:Co. This data were recently obtained by
Walter et al. at the University of North Carolina [41]. The
inventor shows that these data can be quantitatively explained by
the magnetic pair-breaking effect on superconductivity with a
mean-field transition temperature of 645 K and
2.DELTA./k.sub.BT.sub.c0=3.6. This is in excellent agreement with
independent electrical and single-particle tunneling data shown
above.
[0150] It is known that Raman scattering has provided essential
information about the electron-phonon coupling and the electronic
pair excitation energy in the high-T.sub.c cuprate superconductors
[42, 43, 44]. The anomalous temperature dependent broadening of the
Raman active B.sub.lg-like mode of 90 K superconductors
RBa.sub.2Cu.sub.3O.sub.7-y (R is a rare-earth element) allows one
to precisely determine a superconducting gap at
2.DELTA.=40.0.+-.0.8 meV [43]. Moreover, it was found that the
threshold temperature marking the softening of the B.sub.lg mode
with 2.DELTA.<h.omega.<2.2.DELTA. coincides with T.sub.c, and
the mode softens further for lower temperatures. The pronounced
softening observed only for the B.sub.lg mode is due to the fact
that the phonon energy of the B.sub.lg mode is very close to
2.DELTA. and the mode is strongly coupled to electrons [43, 45]. It
should be emphasized that such a softening effect is observable
only for those phonon modes with their energies very close to
2.DELTA..
[0151] In FIG. 11A, the inventor plots the temperature dependence
of the frequency for the Raman-active B.sub.lg mode of a 90 K
superconductor YBa.sub.2Cu.sub.3O.sub.7-y. The figure is reproduced
from Ref. 42. It is apparent that the frequency decreases linearly
with increasing temperature above T.sub.c=90 K, and that the mode
starts to soften below T.sub.c. Such a temperature dependence of
the frequency above T.sub.c is caused by thermal expansion. The
temperature dependence of the frequency will become more pronounced
at higher temperatures since the magnitude of the slop
-dln.omega./dT is essentially proportional to the lattice heat
capacity that increases monotonously with temperature. The
significant softening of the mode below T.sub.c occurs only if the
energy of the Raman mode is very close to 2.DELTA. and the
electron-phonon coupling is substantial [44], as it is the case in
the 90 K superconductor YBa.sub.2Cu.sub.3O.sub.7-y [42, 43, 44]. In
order to see more clearly the softening of the mode, I show in FIG.
11B the difference of the measured frequency and the linearly
fitted curve above T.sub.c. It is clear that the softening starts
at T.sub.c and the frequency of the mode decreases by about 9
cm.sup.-1 at 5 K.
[0152] FIG. 12 shows the temperature dependence of the frequency
for the Raman active G-band of single-walled carbon nanotubes
containing different concentrations of the magnetic impurity Ni:Co.
The data are from R. Walter et al. at the University of North
Carolina [41]. It is remarkable that the frequency shows a clear
tendency of softening below about 630 K in the sample with 0.2%
Ni:Co impurity. Above 630 K, the frequency decreases linearly with
increasing temperature similar to the behavior in
YBa.sub.2Cu.sub.3O.sub.7-y (FIG. 11A). The merging of the curves in
FIG. 12 at high temperatures suggests that the divergence of the
curves at low temperatures is not due to a difference in the mean
chirality distribution of the nanotube bundle.
[0153] In order to see more clearly the softening of the mode, the
inventor shows in FIG. 13 the difference between the measured
frequency and the linearly fitted curve above the kink temperatures
(e.g., above 630 K for the sample containing 0.2% Ni:Co). It is
remarkable that the results shown in FIG. 13 are similar to that
shown in FIG. 11B. This suggests that the softening of the Raman
active G-band in the SWNTs may have the same microscopic origin as
the softening of the Raman active Big mode in
YBa.sub.2Cu.sub.3O.sub.7-y. This explanation is plausible only if
the phonon energy of the G-band is very close to 2.DELTA.. Indeed,
the phonon energy of the G-band is 200 meV, very close to
2.DELTA.=200 meV deduced from the tunneling spectrum and the
electrical breakdown experiment. Therefore, it is very likely that
the softening of the Raman active G-band in the SWNTs is related to
the superconducting transition.
[0154] From FIG. 13, one can clearly see that the softening starts
at about 632 K for the sample containing 0.2% Ni:Co, at about 617 K
for the sample containing 0.45% Ni:Co, and at about 554 K for the
sample containing 1.3% Ni:Co. By analogy to the result shown in
FIG. 11B, the inventor can assign the mean-field transition
temperature T.sub.c0=632 K, 617 K, and 554 K for the samples
containing 0.2%, 0.45%, and 1.3% Ni:Co, respectively.
[0155] In FIG. 14, the inventor shows T.sub.c0 as a function of the
magnetic impurity (Ni:Co) concentration. It is striking that
T.sub.c0 decreases with increasing the magnetic concentration. The
observed T.sub.c0 dependence on the magnetic concentration is very
similar to the theoretically predicted curve based on the magnetic
pair-breaking effect on superconductivity [23]. This gives further
support that the softening of the Raman active G-band in the SWNTs
is related to the superconducting transition around 600 K.
Extrapolating to the zero magnetic-impurity concentration, one
finds T.sub.c0=645 K. Using .DELTA.=100 meV and T.sub.c0=645 K, one
calculates 2.DELTA./k.sub.BT.sub.c0=3.6, very close to that
expected from the weak-coupling BCS theory. It is also remarkable
that the magnitude of the gap deduced from the Raman data is in
excellent agreement with that inferred from a tunneling
spectrum.
[0156] It is known that the resistance of 1D superconductors is
finite below the mean-field superconducting transition temperature
T.sub.c0 due to a large quantum phase slips [19]. In the smallest
diameter SWNT with d=0.42 nm, the mean-field superconducting
transition temperature T.sub.c0 was found to be about 15 K [46].
The temperature dependence of the resistance for the 1D
superconductor is in good agreement with the theoretical
calculation [46]. In FIG. 15A, the inventor plots the resistance as
a function of T/T.sub.c0 for the smallest diameter SWNT. The data
are extracted from Ref. [46]. It is apparent that the resistance
increases more rapidly above 0.5 T.sub.c0 and flattens out towards
T.sub.c0. The resistance at T.sub.c0 appears to be about four times
larger than that at 0.5T.sub.c0. Below 0.5T.sub.c0, the temperature
dependence of the resistance can be well fitted by a power law:
R(1)=R.sub.o+AT.sup.{acute over (.upsilon.)}, as demonstrated in
FIG. 15B. Here R.sub.o is contributed from the contact resistance
and the intrinsic resistance that arises from the quantum phase
slips. From the fit, one finds that the power .beta.=1.77.+-.0.18.
The theory of quantum phase slips in quasi-1D superconductors [19]
predicts that .beta.=2.mu.-3, where .mu. is a quantity that
characterizes the ground state. The resistance at zero temperature
can approach to zero when .mu.>2, but is finite when .mu.<2.
Disorder can lead to weak localization of Cooper pairs and thus
make .mu.<2 [19].
[0157] In FIG. 16, the inventor shows temperature dependence of the
resistivity for a SWNT rope. The data are extracted from Ref. 47.
Below 200 K, the resistivity is nearly temperature independent,
which suggests that the measured resistance is contributed only
from metallic SWNTs. Since the resistance for semiconducting
chirality tubes is larger than that for metallic chirality tubes by
several orders of magnitude [48], any current paths which include
semiconducting chirality tubes are "shortened" by current paths
which consist of only metallic chirality tubes. Considering the
fact that two thirds of the tubes have semiconducting chiralities,
the intrinsic resistivity of the metallic chirality tubes must be
much smaller than that shown in FIG. 16. The contact barriers among
the metallic chirality tubes may contribute to the resistance that
increases weakly with decreasing temperature. The nearly
temperature independent resistance observed below 200 K might be
due to the competing contributions of the barrier resistance and
on-tube metal-like resistance. Above 200 K, the resistivity
increases suddenly and starts to flatten out above 550 K. Such a
temperature dependence of resistivity is similar to that shown in
FIG. 15A, and agrees with quasi-1D superconductivity at about 600
K.
[0158] FIG. 17 shows temperature dependence of resistance for a
single-walled nanotube with d=1.5 nm. The data are extracted from
Ref. 49. The distance between the two contacts is about 200 nm and
the contacts are nearly ideal with the transmission probability of
about 1 [49]. It is remarkable that the temperature dependence of
the resistance can be fitted by a power law
R(T)=R.sub.o+AT.sup.{acute over (.upsilon.)} with
.beta.=1.71.+-.0.23. The power .beta. for the 1.5 nm SWNT is nearly
the same as that for the 0.4 nm SWNT, which has been proved to be
superconducting. Comparing FIG. 17 with FIG. 15, one could infer
that T.sub.c0 for the 1.5 nm SWNT is above 600 K. It should be
mentioned that, within the Fermi-liquid picture, both
electron-phonon backscattering and umklapp electron-electron
scattering lead to a resistivity which is linearly proportional to
temperature [50, 51]). Therefore, it is difficult to explain the
observed temperature dependence of the resistance if the SWNT were
not a quasi-1D superconductor.
[0159] The data shown in FIG. 17 can also rule out Luttinger-liquid
behavior. Phonon backscattering in Luttinger-liquid leads to
semiconductor-like electrical transport at low temperatures and
metal-like transport with .beta.<1 at high temperatures [52].
This is in sharp contrast with the data shown in FIG. 17.
Qualitatively, tunneling spectra in both SWNT and MWNT agree with
either the Luttinger-liquid theory or the environmental Coulomb
blockade theory [34, 53]. The Luttinger-liquid theory [35] predicts
that if .alpha..sup.bulk=0.37, then .alpha..sup.end =0.94, where
.alpha..sup.bulk/.alpha..sup.end is the exponent of power law in
tunneling spectrum for the electron tunneling into the bulk/end of
the Luttinger-liquid. But experiments [34] showed that
.alpha..sup.bulk=0.37 and .alpha..sup.end=0.6, in disagreement with
the prediction of the Luttinger-liquid theory. Moreover, recent
calculation [54] shows that the Luttinger parameter in SWNTs
remains close to its free fermionic values of 1, even for larger
values of doping. This implies that .alpha..sup.bulk.about.0. Thus,
only the environmental Coulomb blockade theory is able to explain
the tunneling data [34].
[0160] Now a question arises: What is the pairing mechanism
responsible for such high superconductivity in carbon nanotubes,
and why does the smallest SWNT have such a low T.sub.c0? A
theoretical calculation showed that superconductivity as high as
500 K can be reached through the pairing interaction mediated by
acoustic plasmon modes in a quasi-one-dimensional electronic system
[55]. The calculated T.sub.c as a function of the areal carrier
density for InSb wires of the cross sections of 50 nm.times.10 nm
and 80 nm.times.1 nm is re-plotted in FIG. 18. The theoretical
calculation indicates that the highest T.sub.c occurs at a doping
level where the first 1D subband is nearly occupied, and that
superconductivity decreases rapidly with increasing the carrier
density. This is because an increase of the carrier density raises
the Fermi level so that more transverse levels are involved,
diminishing the quasi-1D character of the system. For a metallic
single-walled nanotube with d>1 nm, two degenerate 1D subbands
are partially occupied by hole carriers with the carrier
concentration in the order of 10.sup.19/cm.sup.3. This is the most
favorable condition for achieving high-temperature
superconductivity within the plasmon-mediated mechanism [55]. On
the other hand, the smallest SWNT has a carrier density of
3.4.times.10.sup.23/cm.sup.3, as estimated from the measured
penetration depth (3.9 nm) and the effective mass of supercarriers
(0.36 me) [46]. One can easily show that 8 transverse subbands
cross the Fermi level in the smallest SWNT, which makes the
plasmon-mediated mechanism very ineffective. This can naturally
explain why the T.sub.c0 in the smallest SWNT is only 15 K.
Interestingly, the value 2.DELTA./k.sub.BT.sub.c0=3.6 deduced for
SWNTs is in remarkably good agreement with the theoretical
prediction [55].
[0161] For multi-layer electronic systems such as cuprates and
MWNTs, high-temperature superconductivity can occur due to an
attraction of the carriers in the same conducting layer via
exchange of virtual plasmons in neighboring layers [56]. Indeed a
strong electron-plasmon coupling in cuprates has been verified by
well-designed optical experiments [57]. For MWNTs, the dual
characters of the quasi-one-dimensional and multi-layer electronic
structure could lead to a larger pairing interaction and a higher
T.sub.c0. It is interesting that the energy gap (pairing energy) in
the carbon nanotubes is close to that (>60 meV) [58] for deeply
underdoped cuprates that would exhibit phase-coherent
superconductivity above room temperature if the effective mass of
carriers in cuprates could be reduced by one order of
magnitude.
EXAMPLES
[0162] The following examples are submitted to illustrate the
benefit and uses of the embodiments taught herein, but not to limit
the claims to any one embodiment or application.
Example 1
[0163] The present invention is a composition and method of
obtaining phase-coherent or nearly phase-coherent high temperature
superconductivity whereby nested metallic chirality layers in MWNT
are formed whereby the resistance can be tuned based on the number
of nested metallic chirality layers--an increase in layers
decreases resistivity (FIG. 19). The most phase coherent embodiment
of the present examples occurs where all the nested layers have
metallic chiralities and the intra-nested tube distance is as small
as possible. This is due to an effective increase in the number of
the transverse channels by the Josephson coupling of adjacent
superconducting layers. The resistance decreases exponentially with
increasing nested superconducting layers. The zero resistance or
phase coherent state can be achieved in a single MWNT that consists
of nested superconducting layers that meet or surpass the minimum
number of nested layers to achieve high temperature
superconductivity.
Example 2
[0164] The present example is a composition and method of obtaining
phase-coherent or nearly phase-coherent high temperature
superconductivity whereby SWNTs are bundled by putting several
metallic chirality SWNTs in parallel and packed adjacent to each
other resulting in a much lower resistance than the sum of the
individual tubes. FIG. 20 shows a decrease in resistance with the
configuration of the resulting bundles. The diameters of the SWNTs
in the bundle are not necessarily identical. The preferred
embodiment of this example occurs where the inter-tube distance is
as close as possible. The Josephson coupling among the tubes can
suppress the QPS and lower the resistance exponentially.
Example 3
[0165] The present example is a composition and method of obtaining
phase-coherent or nearly phase-coherent high temperature
superconductivity whereby several phase-incoherent MWNTs are put in
parallel and packaged in an adjacent configuration, the resulting
bundle has a much lower resistance than the sum of the individual
tubes. FIG. 21 shows the decrease in resistance with the
configuration of the MWNT bundles. The diameters and the numbers of
the adjacent superconducting layers of the MWNTs are independent
and need not be identical. The preferred embodiment of this example
occurs where the inter-tube distance is as close as possible. The
Josephson coupling among the tubes can suppress the QPS thereby
exponentially lowering the resistance approaching the zero
resistance state.
Example 4
[0166] The present example is a composition and method of obtaining
high temperature superconductivity by combining the embodiments
described in example 2 and example 3 whereby a bundle of MWNTs and
SWNTs are combined.
Example 5
[0167] The present example is a composition and method of making
superconducting quantum interferences devices (SQUIDs) that can
operate at room temperature and have superior spatial resolution. A
SQUID can be constructed from two phase-coherent superconducting
MWNTs or from two phase-coherent superconducting carbon nanotube
bundles by intertube crossings, as shown in FIG. 22. Two
phase-coherent superconducting MWNTs are preferred. The intertube
crossings act as Josephson weak links.
[0168] Suitable suspending agents for use in this invention
include, without limitation, polyvinyl alcohol, polyvinyl acetates,
cellulose ethers and finely divided inorganic powders in an
appropriate solvent such as water, alcohols, a hydrocarbon (alkyl,
alkenyl, or aryl), a chlorohydrocarbon (alkyl, alkenyl, or aryl), a
chlorocarbon (alkyl, alkenyl, or aryl), a fluorohydrocarbon (alkyl,
alkenyl, or aryl), a chlorofluorohydrocarbon (alkyl, alkenyl, or
aryl), a chlorofluorocarbon (alkyl, alkenyl, or aryl), a
fluorocarbon (alkyl, alkenyl, or aryl) or mixtures or combinations
thereof.
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[0228] All references cited herein are incorporated by reference as
if fully reproduced. While this invention has been described fully
and completely, it should be understood that, within the scope of
the appended claims, the invention may be practiced otherwise than
as specifically described. Although the invention has been
disclosed with reference to its preferred embodiments, from reading
this description those of skill in the art may appreciate changes
and modification that may be made which do not depart from the
scope and spirit of the invention as described above and claimed
hereafter.
* * * * *