Low-dimensional BEC

The Bose-Einstein condensation (BEC) temperature T_c of Cooper pairs (CPs) created from a general interfermion interaction is determined for a linear, as well as the usually assumed quadratic, energy vs center-of-mass momentum dispersion relation. This explicit T_c is then compared with a widely applied implicit one of Wen & Kan (1988) in d=2+ dimensions, for small , for a geometry of an infinite stack of parallel (e.g., copperoxygen) planes as in, say, a cuprate superconductor, and with a new result for linear-dispersion CPs. The implicit formula gives T_c values only slightly lower than those of the explicit formula for typical cuprate parameters.     

Enhancement of Magnetization in Liquid 3He at Aerogel Interface

A novel feature of condensate state in liquid ³He is predicted theoretically, which consists of spin triplet s-wave Cooper pairs (Higashitani et al. in J. Low. Temp. Phys. 155:83–97, 2009). Such a spin triplet s-wave state will appear inside aerogel near the surface boundary contacting with superfluid ³He-B, and the enhancement of magnetization due to s-wave state is theoretically expected (Nagato et al. in J. Phys. Soc. Jpn. 78:123603, 2009; Higashitani et al. in Phys. Rev. B 85:024524, 2012). In order to detect this proximity effect, we made the interface in columnar glass tube which coated with 2.5 layer ⁴He, and set a saddle shape NMR coil very near the interface. At 7 bar, we found that superfluidity in liquid ³He inside aerogel never occurred, even at considerably low temperatures. At 24 bar below T/T _c =0.392, we observed no decrease of magnetization with decreasing temperatures. This phenomenon might be due to spin triplet s-wave Cooper pairs.     

The Viscosity Anomaly Near the Lower Critical Consolute Point

Shear viscosity measurements for a critical mixture of 3-methylpyridine + heavy water near a lower critical consolute point are reported. The background contribution was determined from viscosity measurements of mixture at a noncritical composition. In the entire investigated temperature range T _c – T 15.6 K, the viscosity of the critical mixture exceeds the background contribution, and the critical enhancement is important. The increase of the viscosity near critical is found in the temperature range T _c–T 1.82 K. The critical exponent y = 0.0415 ± 0.002 and the wave number Q = (0.40 ± 0.07) nm^–1 are determined.     

On the Bose-Einstein condensation of nonzero-momentum cooper pairs. A second-order phase transition

Based on the BCS Hamiltonian, the normal-to-super phase transition is investigated, approaching the critical temperatureT _c from the high-temperature side. Nonzero-momentum Cooper pairs, that is, pairs of electrons (holes) with antiparallel spins and nearly opposite momenta aboveT _c in the bulk limit, are shown to move like independent bosons with the energy vs. momentump relation=1/2v_F , where _F represents the Fermi velocity (1/2m* _F ² _FFermi energy). The system of free Cooper pairs undergoes a phase transition of the second order with the critical temperatureT _c given byk _B T _c=1/2(²³ _F ³ n/1.20257)^1/3 wheren is the number density of Cooper pairs. The ratio of the jump of the heat capacity, C, to the maximum heat capacity,C _s, is a universal constant: C/C _s=0.60874; this number is close to the universal constant 0.588 obtained by the finite-temperature BCS theory. The physical significance of these results is discussed, referring to the well-known BCS theory, which treats the many-Cooper-pair ground state exactly and the thermodynamic state belowT _c approximately. An explanation is proposed on the question why sodium should remain normal down to 0 K, based on the band structures with the hypothesis that the supercondensate composed of zero-momentum electron and hole Cooper pairs is electrically neutral.     

A New Method for the Estimation of Hc2 Anisotropy in Polycrystalline MgB2 Samples

By using isothermal magnetization measurements in polycrystalline MgB₂ samples, we estimate the H ^c _c2 in the interval [0, T _c]. By combining these measurements to the estimated H ^ab _c2 from the onset of the diamagnetic transition in isofield and isothermal magnetic measurements, an estimation of the anisotropy parameter can be achieved. The H ^c _c2 values coming from high quality polycrystalline samples agrees nicely to those obtained on single crystals. Our results show a temperature variation of the (T ) = H ^ab _c2/H^c2 with (T _c) 3.     

Tc Harmonics in the Subperoxide Model–The Musical Superconductors

The oxide T _c code appears to be decipherable in terms of subperoxide quantization with T _c =666/q. Besides quantized limits in O ^– hole creation through overoxidation (Ox), reductive selfdoping (Red) can be quantitatively understood on this model and correlated to volume expansion effects. Mobile O charge order commensurabilities supply a comprehensive explanation for T _c harmonics, plateaus or variable selfdoping, resolving contradictions concerning doping type or charge transfer.     

Upper critical field of high-T c oxides: Evidence for 2e Bose liquid

We measure and theoretically describe the upper critical field, H_c ²(T), of BSCCO — 2212 crystals with T_c > 92K by the use of the out-of-plane resistivity in magnetic fields (H ab) up to 15T. The empirical procedure is proposed allowing us to extrapolate the H_c ²(T) curve up to H_c ² 230T and t/t _c 0.35 which is independent of the choice of the R/R_N ratio. We found that H_c2(T) does not follow the conventional theory with or without fluctuations and the magnetic scattering, but is consistent with the prediction based on the Bose-Einstein condensation of charged bosons formed aboveT _c . Our results together with several other measurements of H _c 2 and with the heat capacity data provide an evidence for the possibility of 2 _e Base liquid ground state of high-T _c oxides.We highly appreciate the enlightening discussions with Sir Nevill Mott, P. Edwards, J. Cooper, N. Hussey, J. Loram, A. Mackenzie, and K. Ziebeck.     

Surface Effect on Spatial Length-Scales in a Two-Gap Superconductor

The healing of two-band superconductivity near its interface is studied. It is demonstrated that the restoration of superconductivity gaps in the immediate vicinity of the interface is governed by two length scales: the first one diverges at critical temperature T _c , while the second one diverges at T _c+<T _c . By moving away from the boundary, the temperature dependencies of characteristic lengths change so that singularity at T _c+ becomes removed in the bulk by arbitrary weak interband coupling. The asymptotes for the spatial behavior of gaps have been found analytically near the surface and approaching the bulk state.     

The possibility of increasingTc in oxide high-Tc superconductor films: Interaction with elastic fields of defects

The influence onT _c of dilatation centers (DC) as elastic defects near the surface or in thin films of oxide high-T_c superconductors is considered. The distribution function ofT _c in this case was obtained. This is the Lorentzian with center shifted to largerT _c values. The half width of theT _c distribution n (n is the concentration of DC) is larger than its center shift and corresponds to the increase ofT _c fluctuations near the surface. As a result, a continuum percolation behavior with increasing critical temperature percolation levelT ^(c) near the surface appears. The inequalityn>T ^(c)>T _c ^initial is fulfilled. ForT>T ^(c) the quasi-2D Josephson media takes place where a finite superconductive domain withT _c ^local >T ^(c) exists. The influence of DC considerably increases for strong DC such as off-center impurity ions.     

Fluctuations of the Order Parameter''s Phase in Layered Superconductors

The influence of the quantum fluctuations of the order parameter's phase on the critical temperature T _c is studied for a Josephson coupled layered superconductor. Two characteristic critical temperatures exist for a system, namely the superconducting critical temperature T ⁽²⁾ _c for a single layer estimated by the mean-field theory and the transition temperature for the outset or the superconducting phase coherence T* _c . The true critical temperature T _c is shown to vary inside the intervals T* _c T _c T ⁽²⁾ _c . For a strong quantum phase fluctuation limit, the superconducting layers become decoupled.     

Upper Critical Field and Specific Heat of Cuprates

A representative set of magnetotransport measurements in novel superconductors is analyzed. The resistive upper critical field, H _c2 (T) of many cuprates, of superconducting spin-ladders, and organic (TMTSF)2X systems has a universal nonlinear temperature dependence H _c2 (T_c – T)^3/2 in a wide temperature interval near T _c, while its low-temperature behavior depends on the chemical formula and sample quality. The unusual H _c2(T) is described as the Bose–Einstein condensation field of preformed pairs. Its universal temperature dependence follows from the scaling arguments. Controversy in the determination of H _c2 (T) from the resistivity and specific heat measurements is resolved in the framework of the charged Bose-gas model with the impurity scattering. It is shown that specific heat shows two anomalies. The high-temperature anomaly is strong and shows only weak shift with applied field. The low-temperature anomaly corresponds to resistive transition and is very weak in agreement with the experiments. Both anomalies coincide at H = 0.     

Theoretical investigation of the transition temperature of dirty proximity-effect sandwich systems

The influence of impurities and of an interface barrier on the critical temperature of a superconductor-normal (SN) metal sandwich is studied in the Cooper limit. The investigations are based on new equations which allow us to deal with inhomogeneous, dirty superconducting systems near the critical temperature. In contrast with previous treatments, it is shown that at finite film thicknesses,T _c is not only dependent on the N to S thickness ratio, but also on the absolute thickness values, the transmission probability of the interface barrier, and the mean free electron paths. Our results permit the determination of the stay probabilities of McMillan 's tunneling model and the effective length of de Gennes' extended boundary condition on the integral kernel which determinesT _c. Finally, it is shown how the conventional Cooper limit result forT _c by de Gennes is approached.     

Low-temperature magnetic and electromagnetic studies of Y-Ba-Cu-O: Agx Ceramic superconductor

Magnetization and magnetic relaxation measurements have been studied at 4.2 K on YBa₂Cu₃O_7–:Ag _x (x=0 to 1.2) superconducting samples prepared by a coprecipritation technique. Remanent magnetization and hysteresis loops were found to be increased on Ag addition. Transport current density (J _c) was enhanced with the addition of Ag concentration. Flux creep rate was also increased with increase in Ag addition resulting in stronger pinning potential. Microwave-induced d.c. voltage measurements show a reduction of weak links with increase in Ag concentration. The enhancement of transportT _c is attributed to the stronger Josephson current paths due to the reduction of the total number of weak links after Ag addition.     

Enhancement of superconductivity in Pb-Bi-Sn and Pb-Bi-In alloy filaments produced by glass-coated melt spinning

The enhancement ofT _c in Pb-Bi-Sn and Pb-Bi-In system alloy filaments produced by glass-coated melt spinning was investigated as a means of producing a new type of superconducting filament with highT _c. Long filaments of Pb-Bi-Sn alloy withT _c higher than 10 K and Pb-Bi-In alloy withT _c higher than 9 K were obtained from the molten state at a temperature of 1500 K with a winding speed of 2.63 m sec^–1. For example, a Pb₄₅Bi₃₅Sn₂₀ filament withT _c of 10.1 K was 15 m in diameter and polycrystalline with a grain size of 100 nm. The structure of the filament was a mixture of , tin and bismuth phases and a metastable phase of mixed structure of bismuth and supersaturated solid solution of tin in -phase was detected. TheT _c of the filament decreased on heat treatment. A metastable phase of mixed structure of bismuth and -phase was also detected for a Pb₄₅Bi₄₅In₁₀ filament withT _c of 9.3 K. As the metastable phase for the Pb-Bi-In filament was more unstable than that for the Pb-Bi-Sn filament, theT _c of the filament was drastically decreased by heat treatment. The metastable phase was considered to play an important role in the enhancement ofT _c for Pb-Bi-Sn and Pb-Bi-In alloy filaments.     

Measurements of the isochoric heatc v at the critical point of SF6 under microgravity: Results of the German Spacelab Mission D2

During the Second German Spacelab Mission D2 (April 26 to May 6, 1993) the isochoric specific heatc _v of SF₆ was measured along the critical isochore under microgravity conditions with a newly developed scanning radiation calorimeter. This calorimeter provided the possibility to perform comparable heating and cooling runs with variable ramp rates since the spherical sample cell was heated and cooled only by radiation. During the experimental time of 220 h, 11 heating and cooling runs with different ramp rates were performed in a temperature range ofT–T _c=±6 K. ApproachingT _c by cooling from the homogeneous one-phase region avoided significant temperature and density gradients in the fluid, which would have distorted the integral measurement ofc _v. The inhomogenities introduced by a finite ramp rate were greatly reduced by the fast dynamic temperature propagation (critical speeding up). Thec _v data achieved with slow cooling runs are in remarkably good agreement with the theoretical prediction more than one order of magnitude closer to the critical point than anyc _v measurements done so far. The preliminary value for the critical exponent is 0.107±0.02, and for the amplitude ratio we obtainedA ^–/A ⁺=1.94±0.07. In contrast to the cooling runs, the heating runs showed a strong hysteresis ofc _v. A comparison to 1g measurements is provided.Invited paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, USA.     

The Attractive Hubbard Model in 2-D: Is It Capable of Describing a Pseudogap and Preformed Pairs?

Deviations from Fermi liquid behavior are well documented in the normal state ofthe cuprate superconductors, and some of these differences seem to be related topretransitional features appearing at temperatures above T _c. The observationof a pseudogap, e.g., in ARPES experiments, is a familiar example of this physics. Onepotential explanation for this behavior involves preformed pairs with finite lifetimesexisting in the normal state above T _c. In this way, two characteristictemperatures can be established. A higher one T* at which pairs begin toform and the actual T _c at which a phase-coherent superconducting phaseis established. In order to test these ideas we have investigated the negative UHubbard model in two dimensions in the fully self-consistent ladder approximation atlow electron densities. In the non-self-consistent version of this theory the systemalways shows an instability toward Bose-condensation of infinite lifetime pairs. In contrastto this, pairs obtain a finite lifetime due to pair–pair interaction and thesharp two-particle bound state is strongly lifetime broadened when self-consistency isapplied. A quasiparticle scattering rate which varies linearly with temperature is alsofound. The fully self-consistent calculation we were able to perform employed ak -averaged approximation in which the self-energyloses its k -dispersion due to ak -average. This approximation is found to preservethe essential physics.     

Simultaneous ac Susceptibility and Specific Heat Measurements of YBCO Ceramics

Simultaneous ac magnetic susceptibility and specific heat studies of YBCO ceramics permitted the correct correlation of the corresponding critical temperatures. The midpoint of the real component () and the maximum of the imaginary component () of ac susceptibility curves confirmed the T _c = 92 K critical temperature value determined by dc resistance measurements. The specific heat maximum's temperature (T _cc 93.6 K)—-taken as the calorimetric critical one—fell between T _c and T* (the pseudogap onset temperature). We suggest that T _cc signals the appearance of the first localized coherent pairs, while the temperature T _c marks their percolation. The existence of two different critical temperature values confirms the coexistence of partial coherent and coherent electron pairing phenomena in the region below T _cc of the superconducting phase diagram.     

Growth and Characterization of YBCO Thin Films by Sequential Deposition and Annealing

A novel thin film growth procedure, sequential deposition and annealing (SDA), which contains the advantages of both in situ and ex situ procedures, was proposed. Y₁Ba₂Cu₃O_{7 – x} (YBCO) high temperature superconducting thin films were grown and characterized by the SDA procedure. Purely c-axis-oriented YBCO thin films with no foreign phases and other oriented grains were successfully prepared. The superconducting transition properties of SDA-grown YBCO thin films were measured by measurement of inductance and resistance. The inductance measurements gave a T _c ^onset of 85 K and a T _c of 5 K. The resistance measurements gave a T _c ^onset of 90 K and a T _c of 5 K. Atomic force microscopy studies showed that SDA-grown YBCO thin films had micrometer-size grains surrounded by many nanometer-size grains. The nanometer-size grains in SDA-grown YBCO thin films are responsible for degradation of superconducting transition properties.     

Magnetic and nonmagnetic impurities in some A-15 structure systems. II. Magnetic properties

We present measurements of the susceptibility of the A-15 structure systems NbyPt_100–y–x M _x where M = Fe and Ru (y = 73–78). These measurements correlated with those of the critical temperature T _c permit us to conclude that there is a saturation of the effective number of magnetic impurity atoms and that these atoms are situated on the chains. We find also that the magnetic moment of the Fe atoms depend on the value of y. The high value of the Curie temperature and its variation is discussed with the aid of a model of pairs with antiferromagnetic interaction. In order to describe the formation of the localized moments we have taken into account the effect of the environment around each impurity. Depending on the number and the nature of the nearest neighboring atoms, we deduce a magnetic or nonmagnetic behavior of the impurity. The variation of the moment as a function of the nearest neighbors is explained by supposing electronic redistribution between the atoms, which is the same as supposing an interatomic charge transfer.