What is the highest Tc for phonon-mediated superconductivity?

We suggest that the high-temperature superconductivity can be attributed to the director-roles of the van Hove singularity between an electron-electron interaction and an electron-phonon interaction. The difference between the critical temperature and the pairing temperature is presented, and the Fermi arc, the d-wave symmetry and the poor conductivity, etc., are discussed. In particular, the non-s-wave symmetry is predicted to have the highest T _c for superconductors.      

De Haas-van Alphen effect in unconventional superconductors

A theory of the de Haas-van Alphen effect in type-II p-wave and D-wave superconductors (the latter corresponds to the B _1g one-dimensional representation of group D _4h ) has been developed. Solutions for the order parameter and density of quasiparticle states near the upper critical field have been calculated. If the curve enclosing the extremal cross section of the Fermi surface in the plane perpendicular to the external magnetic field coincides with the line of nodes of the superconducting order parameter, the effect of the transition to the superconducting state on the amplitude of magnetization oscillations is negligible. If the line of nodes is oriented differently with respect to the applied magnetic field, the de Haas-van Alphen oscillations are suppressed in a manner qualitatively similar to the case of conventional superconductors. Zh. éksp. Teor. Fiz. 113, 2174–2192 (June 1998)     

The Ginzburg-Landau expansion and the slope of the upper critical field in superconductors with anisotropic normal-impurity scattering

We carry out the Ginzburg-Landau expansion for superconductors with anisotropic s and d pairing in the presence of anisotropic normal-impurity scattering, which enhances the stability of d pairing with respect to disordering. We find that the slope of the curve of the upper critical field, |dH _c2/dT|_{T c}, in superconductors with d pairing behaves nonlinearly as disorder grows: at low scattering anisotropy the slope rapidly decreases with increasing impurity concentration, then gradually but nonlinearly increases with concentration, reaches its maximum, and then rapidly decreases, vanishing at the critical impurity concentration. In superconductors with anisotropic s pairing, |dH _c2/dT|_{T c} always increases with impurity concentration, finally reaching the familiar asymptotic value characteristic of the isotropic case, irrespective of whether there is anisotropic impurity scattering. Zh. éksp. Teor. Fiz. 112, 2124–2133 (December 1997)     

Magnetic flux structures of composite superconducting structures with d- and s-waves superconductors (d-dots)

Composite superconducting structures with d- and s-wave superconductors, d-dots, can be used as two state devices. Their functions depend on structures of the spontaneous magnetic field, which appears because of the anisotropy of d-wave superconductivity. Solving two-components Ginzburg–Landau equation, we have investigated magnetic field structures for d-dots with smaller and larger holes around the corners of d-wave superconducting region. And we argued the effect of holes on the magnetic structures.     

Relation between vortex excitation and thermal conductivity in superconductors

Thermal conductivity κ _xx(T) under a field is investigated in d _{x2 - y2}-wave superconductors and isotropic s-wave superconductors by the linear response theory, using a microscopic wave function of the vortex lattice states. To study the origin of the different field dependence of κ_xx(T) between higher and lower temperature regions, we analyze the spatially-resolved thermal conductivity around a vortex at each temperature, which is related to the spectrum of the local density of states. We also discuss the electric conductivity in the same formulation for a comparison. Received 8 December 2001 and Received in final form 20 March 2002 Published online 6 June 2002     

-wave nonadiabatic superconductivity

The inclusion of nonadiabatic corrections to the electron-phonon interaction leads to a strong momentum dependence in the generalized Eliashberg equations beyond Migdal's limit. For a s-wave symmetry of the order parameter, this induced momentum dependence leads to an enhancement of when small momentum transfer is dominant. Here we study how the d-wave symmetry affects the above behavior. We find that the nonadiabatic corrections depend only weakly on the symmetry of the order parameter provided that only small momentum scatterings are allowed for the electron-phonon interaction. In this situation, We show that also for a d-wave symmetry of the order parameter, the nonadiabatic corrections enhance . We also discuss the possible interplay and crossover between s- and d-wave depending on the material's parameters. Received 12 May 2000     

Fermionic entropy of the vortex state in d-wave superconductors

In d-wave superconductors the electronic entropy associated with an isolated vortex diverges logarithmically with the size of the system even at low temperatures. In the vortex array the entropy per vortex per layer, S _V , is much larger than k _B and depends on the distribution of the velocity field v _s around the vortex. If there is a first-order transition upon a change of the velocity distribution, then there will be a big entropy jump ΔS _V ∼k _B at the transition. This entropy jump comes from the electronic degrees of freedom on the vortex background, which is modified by the vortex transition. This can explain the big jump in the entropy observed in the so-called vortex-melting transition [A. Junod, M. Roulin, J-Y. Genoud et al., Physica C, to be published], in which the vortex array and thus the velocity field are redistributed. The possibility of the Berezinskii-Kosterlitz-Thouless transition in the 3-dimensional d-wave superconductor due to the fermionic bound states in the vortex background is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 6, 465–469 (25 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Surface electron scattering in d-wave superconductors

A theoretical model of a rough surface in a d-wave superconductor is studied for the general case of arbitrary strength of electron scattering by an impurity layer covering the surface. Boundary conditions for quasiclassical Eilenberger equations are derived at the interface between the impurity layer and the d-wave superconductor. The model is applied to the self-consistent calculation of the surface density of states and the critical current in d-wave Josephson junctions. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 242–246 (10 February 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Critical velocity and event horizon in pair-correlated systems with “relativistic” fermionic quasiparticles

The condition for the appearance of an event horizon is considered in pair-correlated systems (superfluids and superconductors) in which the fermionic quasiparticles obey “relativistic” equations. In these systems the Landau critical velocity of superflow corresponds to the speed of light. In conventional systems, such as s-wave superconductors, the superflow remains stable even above the Landau threshold. We show, however, that, in “ relativistic” systems, the quantum vacuum becomes unstable and the superflow collapses after the “speed of light” is reached, so that the horizon cannot appear. Thus an equilibrium dissipationless superflow state and the horizon are incompatible on account of quantum effects. This negative result is consistent with the quantum Hawking radiation from the horizon, which would lead to a dissipation of the flow. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 2, 124–129 (25 January 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Islands of stability of the d-wave order parameter in s-wave anisotropic superconductors

In this paper we find and present on diagrams in the coordinates of η=2t₁/t₀ (the ratio of the second and the first nearest neighbor hopping integrals) and n (the carrier concentration) the areas of stability for the superconducting spin-singlet s- and d-wave and the spin-triplet p-wave order parameters hatching out during the phase transition from the normal to the superconducting phase. The diagrams are obtained for an anisotropic two-dimensional superconducting system with a relatively wide partially-filled conduction band. We study a tight-binding model with an attractive nearest neighbor interaction with the amplitude V₁, and the on-site interaction (with the amplitude V₀) taken either as repulsive or attractive. The problem of the coexistence of the s-, p- and d-wave order parameters is addressed and solved for chosen values of the ratio V₀/V₁. A possible island of stability of the d-wave order parameter in the s-wave order parameter environment for a relatively strong on-site interaction is revealed. The triple points, around which the s-, d-, and p-wave order parameters coexist, are localized on diagrams. It is shown that results of the calculations performed for the two-dimensional tight-binding band model are dissimilar with some obtained within the BCS-type approximation.     

What is the highest T c for phonon-mediated superconductivity?

We suggest that the high-temperature superconductivity can be attributed to the director-roles of the van Hove singularity between an electron-electron interaction and an electron-phonon interaction. The difference between the critical temperature and the pairing temperature is presented, and the Fermi arc, the d-wave symmetry and the poor conductivity, etc., are discussed. In particular, the non-s-wave symmetry is predicted to have the highest T _c for superconductors.     

wave superconductivity: Analysis of the electronic Raman data of and other cuprates

After briefly recalling the d + s model valid for some anisotropic high T c superconductors, we present a theory of electronic Raman spectra in that model and then compare it with new experimental data obtained for an overdoped Y123 single crystal. The d + s model appears to describe satisfactorily the experimental results, indicating a possible doping dependence of the mixing ratio. We note that the Raman spectrum of the overdoped Bi2212 could also be accounted for by the d + s superconductivity model. The case of Hg1212 (or Hg1223) is reexamined. It appears that the spontaneous breakdown of d-wave symmetry may be rather universal in high T c cuprates. Received: 3 March 1998 / Accepted: 30 April 1998     

Transient photoimpedance response of YBa2Cu3O7−0δ epitaxial films in the mixed state

This paper reports on an investigation of transient photoimpedance response to radiation, in other words, real-time variations of the impedance induced by femtosecond optical pulses in superconducting films transferred to the mixed state by an external magnetic field applied parallel to the c-axis. When the films were in a state characterized by the absence of dc resistivity, the response amplitude increased with the magnetic field faster than expected owing to the contribution of magnetic vortices to the impedance of a superconductor with s-wave pairing of electrons. It turned out that the effect is due to a growth in the effective density of quasiparticle states in the mixed state of a d-wave superconductor. In the absence of magnetic field, however, the response amplitude was higher at lower temperatures, which contradicts the predictions of both models. Possible reasons for this feature in the response as a function of temperature are discussed. Zh. éksp. Teor. Fiz. 116, 1035–1047 (September 1999)     

Impurity scattering in f-wave superconductor UPt 3

We study theoretically the effect of impurity scattering in f-wave (or E_2u) superconductors. The quasi-particle density of states of f-wave superconductor is very similar to the one for d-wave superconductor as in hole-doped high T _c cuprates. Also in spite of anisotropy in Δ( ), both the reduced superfluid density and the reduced electronic thermal conductivity is completely isotropic. Received 11 October 2000     

Correlation between the Hall coefficient,penetration depth,transition temperature,gap anisotropy and hole concentration in layered high-temperature superconductors

We explore the correlation between the Hall coefficient, penetration depth, transition temperature, gap anisotropy and hole concentration in a tight binding model for layered high-temperature superconductors. By adopting the BCS strategy, nearest neighbor intralayer singlet and extendeds-wave pairing cut off at the hole Fermi energy, remarkable agreement with generic experimental facts is obtained. Thus, a cylindrical hole Fermi surface and intralayer extendeds-wave singlet pairing appear to be generic features of the cuprate semiconductors. For high doping levels, however, intralayerd-wave singlet pairing appears to be the stable phase.     

Anomalous proximity effect in d-wave superconductors

The anomalous proximity effect between a d-wave superconductor and a thin disordered normal layer is studied theoretically in the framework of Eilenberger equations. It is shown that disorder of the quasiparticle reflection from this thin layer leads to the formation of an s-wave component localized near the boundary. The angular and spatial structure of the pair potential near the interface is studied. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 478–483 (10 April 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The Ginzburg-Landau expansion and the slope of the upper critical field in disordered superconductors

It is shown that the slope of the upper critical field in superconductors with d pairing drops rapidly with increasing concentration of normal impurities, while in superconductors with anisotropic s pairing increases and reaches the well-known asymptotic level characteristic for the isotropic case. This difference makes it possible, in principle, to employ measurements of H _c 2 in disordered superconductors as an experimental method for determining the type of pairing in high-T _c superconductors and systems with heavy fermions. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 5, 347–352 (10 March 1996)     

Quasi-particle transport in vortex state of nodal superconductors

The quasi-classical approach has proved very useful for studying the vortex state of nodal superconductors like d-wave superconductors in high T_c cuprates. After a brief introduction, we review our work on the thermal conductivity tensor in d-wave superconductors and f-wave superconductors.