Vladimir Z. Kresin

On the critical temperature for any strength of the electron-phonon coupling

Abstract A simple analytical expression describing Tc for any strenght of the electron-phonon coupling λ is derived directly from the Eliashberg equation. The behavior of the energy gap in the limits of strong coupling is studied.

Inhomogeneous superconductivity and the “pseudogap” state of novel superconductors

Abstract Many novel superconducting compounds such as the high T c oxides are intrinsically inhomogeneous systems by virtue of the superconductivity being closely related to the carrier density which is in turn provided in most cases by doping. An inhomogeneous structure is thus created by the statistical nature of the distribution of dopants. At the same time doping also leads to pair-breaking and, consequently, to a local depression of T c . This is a major factor leading to inhomogeneity. As a result, the critical temperature is spatially dependent: T c ≡ T c ( r ) . The “pseudogap” state is characterized by several energy scales: T * , T c * , and T c . The highest energy scale ( T * ) corresponds to phase separation (at T T * ) into a mixed metallic-insulating structure. Especially interesting is the region T c * > T > T c where the compound contains superconducting “islands” embedded in a normal metallic matrix. As a result, the system is characterized by a normal conductance along with an energy gap structure, anomalous diamagnetism, unusual a.c. properties, an isotope effect, and a “giant” Josephson proximity effect. An energy gap may persist to temperatures above T c * caused by the presence of a charge density wave (CDW) or spin density wave (SDW) in the region T > T c * but less than T * , whereas below T c * superconducting pairing also makes a contribution to the energy gap ( T c * is an “intrinsic” critical temperature). The values of T * , T c * , T c depend on the compound and the doping level. The transition at T c into the dissipationless ( R = 0 ) macroscopically coherent state is of a percolation nature.

Multigap structure in the cuprates

Abstract Some of the cuprate superconductors, especially Y1Ba2Cu3O7 are characterized by the presence of different overlapping energy bands. The short coherence length requires the introduction of a multigap structure for these materials. General properties of the two-gap model are described and several new results are presented. The model is characterized by several coupling constants and it requires an unconventional analysis particularly if we are concerned with the relation between the values of the gaps and the strength of the coupling. We find generally that one gap must be karger and the other smaller than in the single gap picture. Furthermore, strong coupling effects will decrease the relative difference in the values of the two gaps. We have applied these ideas to explain the NMR data as well as the anomalous critical temperature and magnetic field behavior of PrxY1−xBa2Cu3O7.

Superconducting state in strong coupling

We consider the behavior of the critical temperature in the limit of strong electron-phonon coupling. The peculiar behavior of the order parameter in this limit allows one to evaluate Tc analytically and directly from Eliashbergs equation. We also consider the effect of Coulomb interaction and the contribution of low phonon modes, the role of lattice instabilities and the relative contribution of phonon and non-phonon interactions.

Effect of low dimensionality on the parameters of high Tc superconductors

Abstract A method of determining the values of main parameters such as the effective mass, the Fermi energy, and the coherence length for the new high Tc superconductors is developed. The method is based on specific heat data. The new Tc materials are low dimensional systems and this feature plays a crucial role in the analysis. The parameters are calculated for La2−xSrxCuO4, x⋍0.2 . Particularly interesting is the small value of the Fermi energy.

On the relation between the energy gap and the critical temperature

Abstract It is shown that the ratio β = ϵ/Tc (ϵ is the energy gap at T = OK) saturates with increasing strength of the electron-phonon interaction; the value βmax is calculated. The special case of a multigap superconductor is discussed. New high-Tc superconductors present a unique oppurtunity to observe a multigap structure.

Effects of the structure of the Fermi surface on the normal and superconducting parameters of the high-Tc oxide superconductors

We have described the major features of the Fermi surfaces of the high-Tc cuprates. The description in momentum space and use of Fermiology allows us to analyze the large anisotropy and multiband structure of the new materials. These properties are crucial because of the extremely small values of the coherence length. The Fermi surface can be reconstructed with the use of experimental data. Based on this method, we have evaluated the parameters such as effective mass, Fermi energy, Fermi velocity, and coherence length and estimated them for La1.8Sr0.2CuO4 and Y1Ba2Cu3O7 with the use of heat capacity and Hall effect measurements.

Manganites at low temperatures and light doping: band approach and percolation

A tight-band model is employed for thee2g orbitals in manganites. It is shown that a large intra-atomic Hund couplingJH and the resulting double-exchange mechanism lead to antiferromagnetic ordering along one of the cubic axes, stabilized by the cooperative Jahn-Teller effect, which further decreases the band energy, of the electrons. As a result, LaMnO3 is a band insulator built of 2D ferromagnetic layers. The critical concentration (xc ≃0.16) for the onset of ferromagnetic and metallic behavior at low temperatures in La1−xSrxMnO3 and the phase transition are treated in a percolation approach.

Dynamical screening and superconducting state in intercalated layered metallochloronitrides

An essential property of layered systems is the dynamical nature of the screened Coulomb interaction. Low-energy collective modes appear as a consequence of the layering and provide for a superconducting-pairing channel in addition to the electron-phonon-induced attractive interaction. We show that taking into account this feature allows to explain the high critical temperatures (T c ∼26 K) observed in recently discovered intercalated metallochloronitrides. The exchange of acoustic plasmons between carriers leads to a significant enhancement of the superconducting critical temperature that is in agreement with the experimental observations.

Pressure and high-Tc superconductivity in sulfur hydrides.

The paper discusses fundamentals of record-TC superconductivity discovered under high pressure in sulfur hydride. The rapid increase of TC with pressure in the vicinity of Pcr ≈ 123GPa is interpreted as the fingerprint of a first-order structural transition. Based on the cubic symmetry of the high-TC phase, it is argued that the lower-TC phase has a different periodicity, possibly related to an instability with a commensurate structural vector. In addition to the acoustic branches, the phonon spectrum of H3S contains hydrogen modes with much higher frequencies. Because of the complex spectrum, usual methods of calculating TC are here inapplicable. A modified approach is formulated and shown to provide realistic values for TC and to determine the relative contributions of optical and acoustic branches. The isotope effect (change of TC upon Deuterium for Hydrogen substitution) originates from high frequency phonons and differs in the two phases. The decrease of TC following its maximum in the high-TC phase is a sign of intermixing with pairing at hole-like pockets which arise in the energy spectrum of the cubic phase at the structural transition. On-pockets pairing leads to the appearance of a second gap and is remarkable for its non-adiabatic regime: hydrogen mode frequencies are comparable to the Fermi energy.