Thermodynamic Critical Field Research Articles

THE THEORY OF SUPERCONDUCTIVITY IN CeCu2Si2 AND UBe13 (Ⅱ)——THE CALCULATIONS OF THERMODYNAMIC QUANTITIES

The thermodynamic critical field of superconducting state, the jump of the specific heat at Tc and the behaviors of the specific heat below Tc have been calculated by using the modef and the gap equations given in Ref [1] . It is shown that the critical values of the thermodynamic quantities are qualitatively in agreement with the experimental results,and the behaviors of the specific heat are in accordance with those results of CeCu2Si2 and UBe13 at all temperatures.

Evidence on the nature of superconductivity in La1.85Ba0.15CuO4from specific heat measurements

Information on the nature of the superconducting state in La1.85Ba0.15CuO4 has been obtained from high-precision differential specific heat measurements on superconducting La1.85Ba0.15CuO4, and non-superconducting La2CuO4 and La1.85Ba0.15Cu0.9Ni0.1O4 samples between 1.5 and 300 K. From the very small jump of 0.07 mJ mol-1 K-2 in C/T at Tc approximately 29 K the authors obtain (dHc/dTc)=33 Oe K-1 and Hc(0)=475 Oe, where Hc is the thermodynamic critical field. A condensation of real-space Bose pairs (e.g. bipolarons) is excluded by the author's results, which indicate that a fraction of around 0.06 of the electrons within kTc of the Fermi surface are in Cooper pairs. The estimated electron mass enhancement (1+ lambda ) with lambda approximately 0.82 is lower than expected for conventional phonon-mediated superconductivity with Tc approximately 29 K and indicates that an alternative, possibly excitonic, pair interaction may be involved. Phonon spectra are determined that are in agreement with theoretical predictions, and evidence is obtained for strong high-temperature anharmonicity. A striking anomaly at 58 K in the specific heat of the superconducting compound may indicate a soft phonon mode.

Low-field microwave absorption in the superconducting copper oxides.

A nonresonant microwave absorption has been observed at fields below the thermodynamic critical field, ${H}_{c1}^{(T)}$, in the new copper oxide superconductors. This is associated with flux slippage and allows an estimation of the average area of the uniform phase in the superconducting glass state.

Magnetization of the extreme type II superconductor YBa 2Cu 3O 7 with κ > 100

Magnetization measurements were performed on YBa 2Cu 3O 7 in fields up to 8 T at temperatures close to the superconducting transition T c93 K. The thermodynamic critical field H c was determined from the area between the normal and the superconducting magnetization curves. The initial slope dH c/dT|T c is 190 G/K, and the value of κ is derived using the basic GLAG relations, leading to κ ⋍ 180. The extrapolated specific heat jump at T c is ΔC/T c ⋍ 10 mJ/(K 2mole-Cu), in good ageement with the specific heat measurement, or with the value deduced from the normal state susceptibility. No evidence for an exceptionally large coupling strength (λ) has been observed.

On the surface magnetization in superconducting NaHg 4

The surface magnetization has been obtained indirectly in superconducting NaHg 4, by measuring the Ginzburg-Landau parameter K and the thermodynamic critical field H c , at 2.50 K. Within the Abrikosov approximation, the current-carrying properties of the superconducting sheath have an associated magnetization per unit volume, which can be expressed as a function of k. We have determined this magnetization for cylindrical samples of radius R and size parameters R λ between 2.5 and 20. The dependence of the magnetization on the normalized magnetic field penetration depth gd λ has been established except for the region near the lower critical field.

Magnetic-field penetration depth and material parameters of V-Ag multilayered superconductors.

We have made measurements of the magnetic field penetration depth \ensuremath{\lambda} of V-Ag proximity-coupled multilayers for the first time. The layer-thickness dependence of \ensuremath{\lambda} exhibits a nonmonotonic behavior (existence of a minimum \ensuremath{\lambda}). This is interpreted as a crossover from a single superconductor to a composite one. When the Ag layer becomes thicker, the temperature dependence of \ensuremath{\lambda} begins to deviate from that of usual superconductors, showing that the proximity effect is involved. In addition, from \ensuremath{\lambda} and our previously found upper-critical-field parameters, the Ginzburg-Landau parameter, the thermodynamic critical field at 0 K, and the electronic coefficient of the normal-state specific heat are obtained. The variation of these parameters with layer thickness is also discussed.

A specific heat and magnetization study of highT c ceramic superconductors

From the temperature dependence of the specific heat of the semiconductor La2CuO4 and the high temperature superconductors La1.8Sr0.2CuO4 (T c =37.2 K) and YBa1.9K0.1Cu3O6.9 (T c =91.5 K) in the range 1.5–30 K, a strong similarity of the lowfrequency part of their phonon density of states with a peak around 10 meV could be inferred. In the case of La1.8Sr0.2CuO4 the thermodynamical critical field belowT c has been determined and using the Rutger's formula and the BCS model, a Sommerfeld coefficient γ=9 mJ·mol−1 K−1 was obtained, which, taking into account recent results of band structure calculations leads to an electron-phonon enhancement factor γ=1.3, value compatible withT c =36 K when using McMillan's formula forT c . A systematic study of the magnetization offered evidence for strong flux trapping effects at higher fields and for Meissner shielding by superconducting Josephson currents in fields below 6 mT at 4.2 K.

Flux Pinning in A15 Superconductors

Global pinning force is influenced greatly by microstructures like grain size and third elements, when Nb3 Sn and V3 Ga superconductors are prepared by various different techniques. The structure dependence of flux pinning has been investigated in details. The main flux pinning center was attributed to the grain boundary. Accordinng to the modified shear model proposed by Evetts and Plummer (1985), the global pinning force has been analysed. It was found to have the same magnitude for both NB3Sn and V3Ga. The third elements influenced the specific force as well as the upper critical field. In and Ga made the pinning force increase, while the pinning force decreased by the addition of Ti or Zr. Generally, increasing the critical field resulted in the decrease of specific pinning force. This apparent result is suggested to relate with the change of the thermodynamic critical field. The effect of strain on the pinning force was not direct, but appeared through the change of critical field.

A quasiparticle model for heavy fermion superconductivity

Based on a two-branch quasiparticle model, it has been proposed that the heavy fermion systems can be distinguished into two kinds, i.e. one-heavy-branch system and two-heavy-branch system. It has been inferred that one of the three known heavy fermion superconductors, UPt 3 , belongs to the former kind and the other two, CeCu 2 Si 2 and UBe 13 , belong to the latter. The low-temperature specific heat coefficient, the jump in specific heat and superconducting transition temperature, the order parameters and the thermodynamic critical field of the two kinds of systems have been discussed, and the results are in fair agreement with the experiments.

Superconductivity of triplet bipolarons

Superconductivity of triplet bipolarons has been investigated in a phase analogous to the superfluid A-phase of 3He by use of the broken-symmetry Hartree approximation. The transition temperature T c, the chemical potential and the order-parameters have been obtained, and the specific heat and the thermodynamic critical field have also been calculated. It has been found that there exist two energy gaps in the superconducting state. In the normal phase there also exists a gap, whose magnitude is consistent with the recent experimental evidence of the heavy-fermion superconductor (HFS), UPt 3. Temperature dependence of the critical field of another HFS UBe 13, which is not yet understood, can also be qualitatively accounted for by this model. These show the possibility that triplet bipolarons might be formed in the HFSs.

SUPERCONDUCTING A AND B PHASES IN TRIPLET BIPOLARON SYSTEMS

Superconducting A and B phases in triplet bipolaron system have been treated by useing the selfconsistent broken-symmetry Hartree approximation. The B phase is always more stable than the A phase in the weak coupling case. But in the strong coupling case, owing to the fluctuation feedback effect, the free energy of the A phase can be lower than that of the B phase, or the A-B transition may occur, which is analogous to the superfluid of 3He. The thermody-namic critical field Hc of the stable phase of the system has also been calculated and compared with the upper critical fields of heavy-fermion superconductors, UBe13, UPt3 and URi2Si2. It has been found that Hc can qualitatively account for the abnormal temperature dependences of the upper critical fields of these superconductors.

Thermodynamics of anisotropic superconducting indium analyzed in terms of Eliashberg theory.

Experiments on the change of thermodynamic properties with impurity concentration in indium are presented, which cover the temperature range from 30 mK to the superconducting transition temperature T/sub c/. From an analysis of the T/sub c/ depression with impurity concentration and the temperature dependence of the thermodynamic critical fields in terms of Eliashberg theory, we conclude that the electron-phonon coupling anisotropy is large in indium. The mean-square anisotropy parameter of the usual separable pairing potential is found to be 0.035--0.040. Particular attention is paid to the influence of various experimental error sources and the role of input parameters on the theoretical analysis. It is shown that the concept of coupling anisotropy and anisotropy removal by impurity scattering provides the only consistent description of the experimental results.

BCS-like behaviour in the superconducting state of itinerant antiferromagnetic CrRe alloys

Measurements of the heat capacity and the magnetic susceptibility have revealed BCS-like behaviour in the superconducting state of itinerant antiferromagnetic Cr 1− x Re x alloys for x = 0.30) and 0.26. The thermodynamic quantities, such as electronic heat capacity and thermodynamic critical field have been reproduced with the BCS theory with the energy gap Δ = (1.76 ± 0.05) k B T s, where T S is the superconducting transition temperature for the corresponding system: T S = 3.61 K (2.35 K) for x = 0.30 (0.26).

Free energy of a strong-coupling superconductor with magnetic impurities in Shiba-Rusinov approximation

We evaluate numerically the free energy of a strong-coupling superconductor with paramagnetic impurities in the model of Shiba and Rusinov. Our work is based on a recent formula for the free energy given by Yamamoto and Nagi. This formula is based on the same fundamental expression as used by Schossmann and Schachinger but without their simplfying approximations. Our results are numerically quite different from the previous ones. It is still concluded, however, that the thermodynamic critical field is very sensitive to the model chosen to describe the scattering.

Superconductivity in the Kondo lattice

Superconductivity in the Kondo lattice was theoretically studied in connection with superconductivity in Ce${\mathrm{Cu}}_{2}$${\mathrm{Si}}_{2}$ and U${\mathrm{Be}}_{13}$. To achieve superconductivity in these systems, coherence between Ce ions or U ions is of crucial importance. To take account of the coherence, the periodic Anderson model with a small dispersion of the $f$ band was used. With the use of a single-site approximation for the self-energy of the $f$ electron, the heavy fermion state near the Fermi level was derived. This state is a highly correlated state, and the Coulomb repulsive interaction is strongly reduced. The $f$ electrons are found to be responsible for superconductivity. Both the specific heat in the normal state ${C}_{N}(T)$ and the specific-heat jump $\ensuremath{\Delta}C$ at ${T}_{c}$ are very large, and the ratio $\frac{\ensuremath{\Delta}C}{{C}_{N}({T}_{c})}$ has the BCS value in the weak-coupling approximation. The thermodynamic critical field is very high.

Specific heat and magnetic susceptibility of nearly stoichiometric and homogeneousNb3Al

A15-type Nb/sub 3/Al has been characterized in the recent past as a ''high-T/sub c/, low-..gamma.. superconductor,'' where ..gamma.. is the electronic specific-heat coefficient. We show that this statement should be revised, previous analyses simply reflecting the imperfect metallurgical state. We succeeded in preparing homogeneous, nearly stoichiometric, bulk Nb/sub 3/Al and reinvestigated the specific heat (from 1 to 50 K) and the magnetic susceptibility (19--300 K) in the highly ordered and a slightly disordered condition. The new results show that ordered Nb/sub 3/Al exhibits a high electronic density of states (..gamma.. = 11.4 mJ K/sup -2/ g-at./sup -1/, N(0)approx. =0.91 eV/sup -1/ atom/sup -1/ spin/sup -1/). Information is provided on the moments of the phonon spectrum and those of the electron-phonon spectral function, the thermodynamical critical field, and the energy gap 2..delta..(0). The present experiments further establish only weak exchange enhancement of the susceptibility; spin fluctuations may therefore be safely neglected. Specific-heat data are also reported for the neighboring sigma-phase Nb/sub 2/Al.

Impurity and spin-fluctuation effects in antiferromagnetic superconductors

We derive the superconducting density of states ${N}_{s}(\ensuremath{\omega})$ of an antiferromagnetic superconductor in the presence of impurities and spin fluctuations. We use a self-consistent ansatz for the Green's function $G$ and our previous mean-field-theory results. ${N}_{s}(\ensuremath{\omega})$ depends on four functions of frequency: the renormalized frequency $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}$, gap $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}$, molecular field ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{H}}_{Q}$, and "pseudogap" $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Omega}}$, Equations for these four parameters are set up in general and solved for the case of elastically scattering impurities and spin fluctuations. In the absence of any disorder the density of states has structure at the gap frequency $\ensuremath{\Delta}$ and at $\ensuremath{\omega}=|\ensuremath{\Delta}\ifmmode\pm\else\textpm\fi{}{H}_{Q}|$, where ${H}_{Q}$ is the (screened) molecular field. Most of our numerical work for dirty superconductors is based on a "quasi-three-dimensional" approximation which appears to be reasonable, although it underestimates gaplessness and overestimates the strength of the subsidiary peaks at $|\ensuremath{\Delta}\ifmmode\pm\else\textpm\fi{}{H}_{Q}|$. We find in this approximation that magnetic impurities behave as might be expected but that nonmagnetic impurities can make an antiferromagnetic (AF) superconductor gapless at moderate concentrations. As the concentration is increased still further, the nonmagnetic impurities "screen" out the molecular field, a gap reopens, and ${N}_{s}(\ensuremath{\omega})$ obtains its BCS value. In the process of solving for ${N}_{s}(\ensuremath{\omega})$, we have simultaneously solved the self-consistent equations for $\ensuremath{\Delta}$ (as well as ${H}_{Q}$) as a function of temperature $T$ for dirty superconductors. We find that both $\ensuremath{\Delta}$ and the thermodynamic critical field ${H}_{c}$ exhibit structure at the magnetic ordering temperature ${T}_{M}$. As in the case of our previous mean-field-theory results, the behavior of ${H}_{c}$ is similar to that of ${H}_{c2}$, observed in the ternary compounds. When spin-fluctuation effects are included, ${N}_{s}(\ensuremath{\omega})$ and its derivative are found to exhibit structure at the spin-wave frequencies. In analogy with phonons in strong-coupling superconductors, this observation suggests that a measurement of ${N}_{s}(\ensuremath{\omega})$ in AF superconductors can provide detailed information about the dynamic structure factor for the localized spins.

Atomic disorder and superconductivity in A15 materials

The validity of a modified linear chain model for describing the properties of A15 superconductors is discussed in detail. Using this simple model for the electronic density of states, we calculate the critical temperature and the Fermi level as functions of atomic disorder with concentrationc within the framework of the BCS theory. Thereby the experimentally observed saturation effect of the critical temperature is reproduced by taking into account the contribution of three-dimensional electronic states. The microscopic versions of the Ginzburg-Landau equations for systems with a strongly varying electronic density of states and a strongly varying electron velocity are derived for clean and dirty superconductors in order to calculate the Ginzburg-Landau parameter, the coherence length, the penetration depth, and the upper critical field as functions of atomic disorder. It is shown that these quantities depend strongly on the values inserted for the mean free electron pathl(c). Good agreement between theoretical and experimental results is obtained by an appropriate choice ofl(c). In contrast, the thermodynamic critical field is nearly independent ofl(c). In all cases we derive a depression of the pinning forces and the critical current densities with increasing atomic disorder in good agreement with the experiments.

Thermal expansion of La 3S 4 at low temperatures

The thermal expansion of the superconductor La 3S 4 has been investigated on a single crystal by a capacitive method between 1.6 and 14 K. The relative length change shows a well pronounced second order phase transformation near 8.05 K, which is caused by the superconducting transition. From the calculated linear thermal expansion coefficient we determine the pressure coefficient of the transition temperature and of the thermodynamic critical field as well as the thermodynamic critical field itself. Furthermore we estimate the electronic, phononic and total Grüneisen parameters. These parameters have been used to discuss on the basis of the McMillan equation the reason for the increase of the transition temperature under pressure.

Thermodynamic properties and fundamental parameters of single crystal Cu 1.8Mo 6S 8

On the single crystal Chevrel phase compound Cu 1.8Mo 6S 8, the specific heat in the normal and superconducting states has been measured from 2 to 15 K at 0 and 90 kOe. Thermodynamic critical field H c(T) has been obtained. Various fundamental parameters are estimated according to the BCS-GLAG theory. The results show that Cu 1.8Mo 6S 8 is a strong coupling superconductor with a large intrinsic GL parameter κ 0.