BACKGROUND OF THE INVENTION 1. Field of the Invention [0002] 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.

[0003] 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.

2. Description of the Related Art [0004] 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.

[0005] 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.

[0006] 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.

[0007] Superconductivity is manifested only below a certain critical temperature called"T," and a critical magnetic field called"Hc,''which vary with the material used. Before about 1986, the highest T, that could be achieved was 23.2 K (-249. 8°C/-417. 6°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.

[0008] 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°C/-321 °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, of 94 K (-179°C/-290°F), was revealed to be YBa2Cu307 (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, of 125 K (-148°C/-234°F).

[0009) 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.

[00010] 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 (-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 (1 D) and/or multi-layer systems.

[0011] 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 + v, where N, n, m are the integers, and v = 0, 1. The tubes with v = 0 are metallic while the tubes with v = 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.

[0012] Indeed, i n a s eries o f five p apers r esident o n t he c ond-mat e-print archive s ince 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.

[0013] 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 Tc in thin superconducting wires.

[0014] 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 27x at some points along the wire, resulting in voltage pulses. The QPS tunneling rate is proportional to exp (-SQPS), where SQPS, in clean superconductors, is very close to the number of transverse channels Nchin the limit of weak damping. If the number of the transverse channels NCh is small, the QPS tunneling rate is not negligible, leading to a finite resistance at low temperatures. For a single-walled nanotube (SWNT), N, : h = 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 To 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.

DEFINITIONS [0015] 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.

[0016] 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.

[0017] Mean-field superconducting transition temperature is the critical temperature below which the electron pairing starts to take place.

[0018] Phase coherent superconducting state: A state with resistance approaching zero.

[0019] Phase incoherent superconducting state: Finite-resistance state below the mean-field superconducting temperature.

[0020] 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.

[00211 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.

[0022] A nanotube is a small tube having a diameter between about 0.42 and about 1000 nanometers.

[0023] A carbon nanotube (CNT) is a nanotube comprising substantially elemental carbon.

[0024] A multiwalled carbon nanotube (MWNT) is a collection of nested CNTs which share a common axis.

[0025] A single walled carbon nanotube (SWNT) is a CNT comprising only one shell or layer.

[0026] A superconducting carbon nanotube (SCNT) is a CNT that superconducts.

[0027] 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.

[0028] 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.

[0029] Both semiconducting and metallic chirality CNTs can be made to superconduct via the doping of carriers into the CNT.

[0030] Superconducting tubes are quasi-ID superconductors and can be Josephson coupled to exhibit less dissipation or resistivity. <BR> <BR> <BR> <BR> <P>[0031] Semiconductingtubes have a semiconducting chiralityandhave theFermi level between the valence and conduction band edge.

[0032] 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 1 in common, where 1 is the minimum of the length of both tubes laid side-by-side. Over the distance 1, one CNT will have analogous points that are separated from analogous points on the second CNT, by the same or nearly the same distance.

[0033] A C NT i s p roximate to another C NT, i f t he t wo C NTs a re c lose t o e ach o ther.

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 1, 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 1.

[0034] 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.

[0035] 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.

[0036] 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.

[0037] 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 jj. 0hm-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.

[0038] 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.

[0039] 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%.

[0040] 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 [0041] 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.

[0042] The p resent i nvention p rovides a c omposition c omprising a m ulti-walled c arbon nanotube, having phase-coherent superconductivity above about 20 K.

[0043] 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.

[0044] The present invention provides a composition comprising a bundle of multi-walled carbon nanotubes, having phase-coherent superconductivity above about 20 K.

[0045] The present invention provides a composition comprising a matrix including bundles of multi-walled nanotubes, having phase-coherent superconductivity above about 20 K.

[0046] The present invention provides a composition comprising a matrix including bundles of single-walled nanotubes, having phase-coherent superconductivity above about 20 K.

[0047] 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.

[0048] The present invention also provides methods of achieving a large positive magnetoresistance in bundles of superconducting carbon nanotubes above about 20 K.

[0049] The present invention also provides superconducting quantum interference devices comprising a composition of this invention.

[0050] The present invention also provides magnetic reading heads comprising a composition of this invention.

[0051] The present invention also provides magnetic switch devices comprising a composition of this invention.

[0052] The present invention also provides magnetic image devices comprising a composition of this invention.

[0053] The present invention also provides conductive elements comprising a composition of this invention.

[0054] The present invention also provides two or more electronic elements interconnected by a conductive element comprising a composition of this invention.

[0055] 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 [0056] The invention can be better understood with reference to the following detailed description together with the appended i llustrative drawings i n which 1 ike e lements are numbered the same: [0057] Figure 1 A depicts the temperature dependence ofthe remnant magnetization for multi- walled nanotubes. After [1]; [0058] Figure 1B depicts the field-cooled susceptibility as a function of temperature in a field of 0.020 Oe. After [1]; [0059] Figure 2 depicts the temperature dependence of the conductance for a multi-walled nanotube rope (reproduced from Ref [3] ) ; [0060] Figure 3A depicts the Hall coefficient versus temperature for a nanotube rope (reproduced from Ref. [3] ); [0061] Figure 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] ) ; [0062] Figure 4 depicts the Hall coefficient component for physically separated tubes (PS) and the component for Josephson-coupled superconducting tubes (JC); [0063] Figure 5A depicts the Hall voltage component for physically separated tubes (PS) at 5 K ; [0064] Figure 5B depicts the Hall voltage component for Josephson-coupled superconducting tubes (JC) at 5 K; [0065] Figure 6A depicts the temperature dependence of the four-probe resistance for a single MWNT with d = 17 nm (reproduced from Ref [20] ) ; [0066] Figure 6B depicts the temperature dependence of the resistance over 10-60 K, which is fitted by R (T = R, + alP. The fitting parameters: Rct = 5.6 (5) kQ, p =-0.65 (9), and a = 29 (4) ka. 65 ; [0067] Figure 7A depicts the temperature dependence of the resistance for a SWNT (data extracted from Ref. [26] ) ; [0068] Figure 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]; [0069] Figure 8 depicts the I-V characteristic observed in a MWNT with d = 9.5 nm. The figure is reproduced from Ref. [30]; [0070] Figure 9 depicts the critical current- (T) for a SWNT rope (data extracted from Ref.

[38] ), solid line represents calculated curve using Eq. 8 and TCo= 580 mK; [0071] Figure 10A depicts the critical currents ic'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] ); [0072] Figure 10B depicts the mean-field critical temperature, TO's, of individual superconducting layers in the MWNTs with d = 9.5 nm and 15 nm, respectively, (To's are calculated using Eq. 9 and assuming ic = il) ; [0073] Figure 11 A depicts the temperature dependence of the frequency for the Raman-active B, g mode of a 90 K superconductor YBa2Cu307 y (data extracted from Ref. [42] ); [0074] Figure 11B depicts the difference of the measured frequency and the linearly fitted curve above Tc ; [0075] Figure 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] ) ; [0076] Figures 13A, B & C depict the difference between the measured frequency and the linearly fitted curve above the kink temperatures (see text); [0077] Figure 14 depicts the To as a function of the magnetic impurity (Ni: Co) concentration in SWNTs ; [0078] Figure 15A depicts the resistance data as a function of TITO for the smallest diameter SWNT with d = 0.42 nm (data extracted from Ref. [46] ); [0079] Figure 15B depicts the temperature dependence of the resistance below 0. 5To (data are well fitted by R (T) = Ro + 70 witho = 1. 77 0.18 ; [0080] Figure 16 depicts temperature dependence of the resistivity for a SWNT rope (data extracted from Ref. [47] ) ; [0081] Figure 17 depicts temperature dependence of the resistance for a single-walled nanotube with d = 1.5 nm (data extracted from Ref. [49] ) ; [0082] Figure 18 depicts the calculated T, as a function of the areal carrier density for InSb wires of the cross sections of 50 nmx 10 nm and 80 nm#10 nm (curves reproduced from the original plot of Ref. [55] ) ; [0083] Figure 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; [0084] Figure 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; [0085] Figure 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 [0086] Figure 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 [0087] 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 o f 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 EF and carrier concentration per carbon n is given by n=0. 02041EFl/d, where the diameter d is in unit of nanometer and the Fermi energy EF is in unit of eV. When the concentration of doped holes or electrons is close to 0. 019/d2 per carbon, the first subband is completely occupied. The preferred diameter of the tube for maximizing superconducting transition temperature is about 1 nm.

[0088] 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.

[0089] 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.

[0090] 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.

[0091] 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.

[0092] 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.

[0093] 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.

[0094] 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.

[0095] 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.

[0096] 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 s een. T his s pectroscopy w ill b e a p owerful d evice t o d iagnose magnetic memory cards, magnetic taps and diskettes, current distributions of chips, and so on.

[0097] 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 c hange o f t he m agnetic fields n ear a b undle o f s uperconducting c arbon nanotubes will lead to a large change in the resistance of the bundle. The magnetic field can be p roduced b y a c urrent o r a p ermanent m agnet. C hanging t he c urrent o r t he d istance 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.

[0098] 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.

[0099] 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.

Transport and Magnetic Properties in Multi-wall Carbon Nanotube Ropes: Evidence for Superconductivity above Room Temperature [00100] 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.

[00101] The inventor first discusses the temperature dependencies of the remnant magnetization M, and the diamagnetic susceptibility for his mult-walled nanotube ropes.

Plotted in Figure 1 are the experimental results which are reproduced from Ref. 1. It is apparent that the temperature dependence of the Mr (Figure) is similar to that of the diamagnetic susceptibility (Figure 1 B) except for the opposite signs. This behavior is expected for a superconductor. The M, was also observed by Tsebro et al. up to 300 K [2]. However, the observation of the M, alone does not give evidence for superconductivity since the M, could be caused by ferromagnetic impurities and/or ballistic transport.

[0102] 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, 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 (Figure 1B). This provides strong evidence that the observed M, in the nanotubes has nothing to do with the presence of ferromagnetic impurities.

(0103] Figure 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 Figure 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.

[0104] 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.

[0105] In Figure 3, the inventor shows the temperature dependence of the Hall coefficient (Figure 3A) and the field dependence of the Hall voltage (Figure 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 Figure 1 and Figure 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.

[0106] 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 + v, where N, n, m are the integers, and v = 0, 1. The tubes with v = 0 are metallic while the tubes with v = 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.

[0107] 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.

[0108] 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 MgB2 [7,8], the low-field Hall coefficient RH in the vortex-liquid state is negative below Tcs reaching a minimum at Tk, and then increasing towards zero with further decreasing temperature. Below the characteristic temperature Tk, 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 Figure 1, Figure 2 and Figure 3A.

[0109] 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. Figure 4 shows both PS (dashed line) and JC (solid line) components. It is apparent that the JC component has a local minimum at Tk 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.

[0110] Similarly, as seen in cuprates and MgB2 [7,8, 9], the Hall voltage VH in the vortex- liquid state is negative, passing through a minimum at Bk, and then increasing towards the normal-state value with further increasing temperature. Below BO, VH tends to zero.

Interestingly, both BO and Bk can be independently obtained from the field dependence of the longitudinal resistivity, as described in Ref. 9.

[0111] 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 Figure 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 Figure 3B. Figure 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 Figure 3 B w ere smoothed. The inventor can see that the field dependence of the JC component is quite similar to that for cuprates and MgB2 [7,8, 9] except that BO in the MWNTs is rather small, which may be due to a weak pinning potential. Figure 5B also indicates that the magnitude of Bk is larger than 5 T, in agreement with the longitudinal magnetoresistance data (see below).

[0112] 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 Bk [9], the inventor finds that Bk 3.0 T at 300 K. Using the relation Bk (T) = Bk (0) ( 1-T/T)'. s 9], T-650 K [1], and Bk (300K) = 3.0 T, one hasBk (5K) = 7.5 T. This could explain why one has not seen the local minimum in VH below 5 T. It is highly desirable to perform the Hall effect experiment up to 15 T to see the crossover field Bk.

[0113] 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 Figure 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].

[0114] 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 = 400 Oe, the temperature dependence of the susceptibility for the nanotube sample (see Figure 8 of Ref.

10) is similar to that for a ceramic cuprate superconductor in a low field (see Figure lOa of Ref. 11). The M (H) curve below H= 10 kOe (see Figure 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 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 C60 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.

Quasi-one-dimensional Superconductivitv above 300 K and Quantum Phase Slips in Individual Carbon Nanotubes [0115] 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 To 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.

[01161 It is known that superconducting fluctuations in one-dimensional (1D) superconductors play an essential role in the resistive transition. Slightly below superconducting transition temperature TCoX 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 To in thin superconducting wires [15, 16,17, 18].

Further, a crossover to an insulating state has been observed in ultra-thin Pbln wires with diameters of the order of 10 nm [15,17] as well as in ultra-thin wires of MoGe [18].

[0117] 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 at some points along the wire, resulting in voltage pulses. The QPS tunneling rate is proportional to exp (-SQps), where SQPS in clean superconductors is very close to the number of transverse channels Nch in the limit of weak damping (see below). If the number of the transverse channels Nch is small, the QPS tunneling rate is not negligible, leading to a non-zero resistance at low temperatures. For a single-walled nanotube (SWNT), Nah = 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 To 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].

[0118] 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] where the attempt frequency Q is given by [14] where L is the length of the wire, 4 is the coherence length, and #/# = (9/#)kB(Tc-T). The barrier energy AF,, is where H 2/871 is the condensation energy and A is the cross-section area of the wire. The condensation energy is equal to N (0) A2/2 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 A. For a metallic SWNT with NCh =2, N (0) A= 4/ (3# aC-Cγo) (Ref. 24), # vF = 1. 5ac_cyo (Ref. 25), where Yo is the hopping integral, r is the radius of the tube, and aC-c is the bonding length.

Using # = #vF/## and the above relations, one can readily show that #Fo#/#= 0.13 Nch and #Fo/# # 0.19 NCh. For MWNTs with N. metallic layers, zIFo fS = 0.26 N. and #Fo/# = 0.38 Nm.

[0119] It was shown that the TAPS is significant only at temperatures very close to and below TCo [14]. At lower temperatures, the finite resistance is caused by MQT and is given by [16], where ß, and (32 are constants, depending on the damping strength. When the damping increases, ß2 decreases. Substituting #Fo#/# = 0. 26nom into Eq. 4, the inventor finds that [0120] From Eq. 5, one can see that SQps # 2Nm in the limit of weak damping where ß2 = 7.2 (Ref. 16). For a stronger damping, ß2 is reduced so that SQPS < 2N#. Moreover, in the dirty limit, SQPS will be further reduced [19] such that SQPS « 2Nm. For a SWNT, N., = 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, Nm = 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 llm (Ref. 28).

[0121] A more rigorous approach to the QPS in quasi-1D superconductors [19] suggests that Sops depends not only on the quantity #Fo#/# but also on the normal-state conductivity a ( Sops oc a'/3). Therefore, one can very effectively suppress the QPS and the resistance below Te0 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.

[0122] Now the inventor discusses the temperature dependence of the resistance observed in nanotubes. Figure 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 1D superconductors can naturally explain this unusual behavior. It was shown that [19], the resistance R # T2µ-3 for kBT# #oI/c, and R becomes independent of temperature and is proportional to I2µ-3 for kBT# #oI/c, where 0. is the quantum flux, c is the speed of light, and 1 is the current. When < 1.5, R increases with decreasing temperature (semiconducting behavior), while p > 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 Tc0.

[0123] Based on the QPS theory, the inventor can readily show that, for #oI/ckB#T#Tc, the four-probe resistance R (T) is R (T) = RCl + aTP (6) where Rct is the tunneling resistance and p = 2p-3. The tunneling resistance is given by RC = RQ/tNCh, where t is the transmission coefficient (t <1) and RQ = h/2e2 =12. 9 kQ is the resistance quantum.

[0124] In Figure 6B, the inventor fit the resistance of the MWNT by Eq. 6. The best fit gives Rc ! = 5.6 (5) kQ, p=-0. 65 (9), and a = 29 (4) kQ K065. The value of Rct suggests that the intrinsic saturation resistance of the tube is 9.7 kQ.

[0125] From the value of 7 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 Nch 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].

[0126] In Figure 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 Figure 7B. The characteristic temperature Y'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 Figure 7A and Figure 7B, one might infer that the mean-field To of this nanotube is well above 270 K.

[0127] From the single-particle tunneling spectrum obtained through two high-resistance contacts (see Figure 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 A = 100 meV in doped metallic SWNTs (EF is about 0.2 eV below the top of the valence band). Using kBTCo = A/1. 76, one finds To = 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].

[0128] Now the inventor explains one of the most remarkable features observed in the carbon nanotubes. At large biases, the current saturates at 19-23 pA 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, theI-Vcharacteristic 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].

[0129] 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-Vcharacteristics of both SWNTs and MWNTs [27,30] are similar to that observed in ultra-thin PbIn superconducting wires (see Fig 8 of Ref. 17). Figure 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 Icl, 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 d V/dI is equal to the sum of the on-tube resistance and the contact resistance. When the applied current increases slightly above I, 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, in the absence of defects. Since the phase slips occur initially near normal regions located around defects in the sample, one expects that Icl should strongly depend on the density of defects and thus on the normal-state resistivity. From Figure 8, one can see that Ic1<0.75Ic.

[0130] According to the BCS theory, the mean-field critical current in the clean limit is given by [23] The superfluid density ns (T = n#2(0)/#2(T), and the normal-state carrier density n = 2N (O) EF = 2N (0) #vFkF = 4kF/A#. Here one has used the relations: N (0) A = 4/(3#aC-Cγo), and AvF = 1. 5ac-cyo as well as E = hvflkl. Substituting the above relations into Eq. 7 yields with Ic (0) = 7. 04Nm kBTc0/eRQ. Here #2(0)/#2(T) follows the BCS prediction, and A (0) tanh~' [1.6 (T, 1)1/2], which is very close to that predicted by the BCS theory. The critical current i, per superconducting layer is then given by [0131] For a SWNT rope, the resistance starts to drop below about 550 mK and reaches a value Rr = 74 Q at low temperatures [38]. The data are consistent with quasi-1D superconductivity with To = 550 mK and Nm = RQ12Rr = 87 (Ref. 38). Substituting these numbers into the expression: Ic (0) = 7. 04NmkBTc01eRQ, one obtains Ic (0) = 2.25 pA, in excellent agreement with the measured Ic (0) = 2.41 usa, as seen from Figure 9. The solid line in Figure 4 is the calculated curve using Eq. 8 and TCO= 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 kQ/pm) 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.

[0132] In Figure 10A, the inventor shows the critical currents i,,'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 ic tends to decrease with decreasing the diameter of the layer, while for d = 15 nm the tendency is just opposite. Plotted in Figure 1 OB is the mean-field critical temperature Two's of individual superconducting layers in the MWNTs, which are calculated using Eq. 9 and assuming ic = icl. It is clear that the calculated Two's are underestimated because ic is always larger than icl, as seen in Figure 8. One can see that Tc0 varies from 430 K to 610 K, in good agreement with the independent resistance data [10]. The broad variation in TCo suggests that TCo depends on doping and the diameters of tubes.

[0133] 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 0. (= 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 20. should have been observed if the phase coherence length of single particles is reasonably larger than zd (the AB effect for the single particle density of states [40] ). If the phase coherence length L deduced from experiment (e. g., L) ~ 300 nm >> zd 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.

[0134] 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 p article with a c harge o f 2 e. Therefore, the W L t heory for s ingle p articles s hould b e 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 0) 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 #d.

[0135] 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 kQ (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 m agnetic flux sensed by t he c arriers i n a 11 t he c onducting 1 ayers s hould b e B # (rout2+rn2)/2, where rO", and riz are the radii of the outermost and innermost conducting layers, respectively, and B is the magnetic field. One can calculate rjn using the relation r)"= rOUt- 0.34 (N",-l) nm. For the MWNT with d = 17 nm, Nm = 17 (see above), leading to rin = 3. 06 nm. From the measured magnetic-field period of 8.2 Tin the MWNT [20], one finds that the magnetic-flux period is 0. 51#o, in quantitative agreement with the thesis that the charge carriers are Cooper pairs with a finite phase coherence length due to the QPS.

Raman Spectroscopie Evidence for Superconductivity at 645 K in Single-wall Carbon Nanotubes [0136] 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 20/kBTo = 3. 6. This is in excellent agreement with independent electrical and single-particle tunneling data shown above.

[0137] 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 cuprate superconductors [42,43, 44]. The anomalous temperature dependent broadening of the Raman active B, g-like mode of 90 K superconductors RBa2Cu307 y (R is a rare-earth element) allows one to precisely determine a superconducting gap at 2A = 40.0 0.8 meV [43]. Moreover, it was found that the threshold temperature marking the softening of the B, g mode with 2A </ ! (o < 2. 2A coincides with Tcx and the mode softens further for lower temperatures. The pronounced softening observed only for the B, g mode is due to the fact that the phonon energy of the B, g mode is very close to 2A 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 2A.

[0138] In Figure 11 A, the inventor plots the temperature dependence of the frequency for the Raman-active B, g mode of a 90 K superconductor YBa2Cu307 y. The figure is reproduced from Ref. 42. It is apparent that the frequency decreases linearly with increasing temperature above Tc = 90 K, and that the mode starts to soften below TC. Such a temperature dependence of the frequency above Tc 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#/dT is essentially proportional to the lattice heat capacity that increases monotonously with temperature. The significant softening of the mode below TC occurs only if the energy of the Raman mode is very close to 2A and the electron-phonon coupling is substantial [44], as it is the case in the 90 K superconductor YBa2Cu307 y [42,43, 44]. In order to see more clearly the softening of the mode, I show in Figure 11B the difference of the measured frequency and the linearly fitted curve above TC. It is clear that the softening starts at TC and the frequency of the mode decreases by about 9 cm~ at 5 K.

[0139] Figure 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 YBa2Cu307 y (Figure l lA). The merging of the curves in Figure 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.

[0140] In order to see more clearly the softening of the mode, the inventor shows in Figure 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 Figure 13 are similar to that shown in Figure 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 B, g mode in YBa2Cu307 y. This explanation is plausible only if the phonon energy of the G-band is very close to 2A. Indeed, the phonon energy of the G-band is 200 meV, very close to 2A = 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.

[0141] From Figure 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 Figure 11B, the inventor can assign the mean-field transition temperature To = 632 K, 617 K, and 554 K for the samples containing 0.2%, 0.45%, and 1.3% Ni: Co, respectively.

[0142] In Figure 14, the inventor shows To as a function of the magnetic impurity (Ni: Co) concentration. It is striking that To decreases with increasing the magnetic concentration. The observed To 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 To = 645 K. Using A = 100 meV and To = 645 K, one calculates 2A1kBTCo = 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.

[0143] It is known that the resistance of 1D superconductors is finite below the mean-field superconducting transition temperature To due to a large quantum phase slips [19]. In the smallest diameter SWNT with d = 0.42 nm, the mean-field superconducting transition temperature To 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 Figure 15A, the inventor plots the resistance as a function of TITO for the smallest diameter SWNT. The data are extracted from Ref. [46]. It is apparent that the resistance increases more rapidly above 0. 5To and flattens out towards Tc0. The resistance at To appears to be about four times larger than that at 0. 5TO. Below 0. 5TO, the temperature dependence of the resistance can be well fitted by a power law : R (T) = RO + AT&num , as demonstrated in Figure 15B. Here 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 ß = 1.77 0. 18.

The theory of quantum phase slips in quasi-lD superconductors [19] predicts that P = 2-3, where u is a quantity that characterizes the ground state. The resistance at zero temperature can approach to zero when u > 2, but is finite when p < 2. Disorder can lead to weak localization of Cooper pairs and thus make < 2 [19].

[0144] In Figure 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 Figure 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 Figure 15A, and agrees with quasi-ID superconductivity at about 600 K.

[0145] Figure 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 powerlawR (I) =Ro +ATßwith ß = 1. 71+0. 23. The power p 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 Figure 17 with Figure 15, one could infer that To 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-lD superconductor.

[0146] The data shown in Figure 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 ß < 1 at high temperatures [52]. This is in sharp contrast with the data shown in Figure 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 abUlk = 0. 37, then αend = 0. 94, where a'"'"7a 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 bulk = 0. 37 and aend = 0. 6, in disagreement with the prediction ofthe 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 bulk ~ 0. Thus, only the environmental Coulomb blockade theory is able to explain the tunneling data [34].

[0147] 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, ? 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 TC as a function of the areal carrier density for InSb wires of the cross sections of 50 nmx 10 nm and 80 nmx 10 nm is re-plotted in Figure 18. The theoretical calculation indicates that the highest T, 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-lD 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 10'9/cm3. 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. 4xl023/cm3, 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 TCO in the smallest SWNT is only 15 K. Interestingly, the value 2A1kBTCo = 3.6 deduced for SWNTs is in remarkably good agreement with the theoretical prediction [55].

[0148] 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 TO. 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 [0149] 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 [0150] 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 (Figure 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 [0151] 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. Figure 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 [0152] 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. Figure 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 [0153] 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 [0154] 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 Figure 22. Two phase-coherent superconducting MWNTs are preferred. The intertube crossings act as Josephson weak links.

[0155] 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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[0157] 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.