On Some Factors Affecting the Critical Temperature in a Two-Band Model of Superconductivity

P Tarasewicz

doi:10.1007/s10948-013-2173-9

Abstract

The influence of a few factors on the critical temperature in a two-band superconducting system is investigated. The system contains conventional Cooper pairs from a wider band (the d-band) as well as local pairs (local bipolarons) from a narrower band (the f-band), which are induced via a pair-exchange potential. These factors are the Coulomb repulsion between f-electrons, the position of the f-band with respect to the bottom of the d-band and two kinds of hopping in the f-band: a single-polaron hopping and a pair hopping. The Coulomb potential turns out to lower the critical temperature from higher values to the pure BCS one. Each of the kinds of hopping is treated by making use of perturbation theory. Pair hopping is incorporated as the first order correction but the hopping of single polarons enters as the second order one. Each of them increases this temperature on its own, however, the hopping of single polarons makes it stronger. The position of the f-band that corresponds to the site energy of a f-electron poses a very interesting case. There appear two peaks at two values of that energy meaning a rapid increase of the critical temperature due to the strong effect of the presence of local electron pairs. In this case one has to do with a purely chemical mechanism of the increase of the critical temperature.

Highlights

For last decades there has been much progress in the discovery of new phenomena in solid state physics
The simplest way was to reconsider the expression for the critical temperature in the BCS theory and take into account the manipulation on the width of the narrow shell around the Fermi level on which the BCS interaction is defined to be nonzero and the magnitude of the coupling constant
There is a multitude of them, for example, Ti4O7, NaxV2O5 or CsSbCl6 and TlF2, which are not superconductors, but their ground state is charged-ordered. Besides some superconductors such as A15, C15, V3Si, Nb3Ge and cuprates such as the tungsten bronzes and the doped bismuthates (Ba1−x KxBiO3 and BaPb1−x Bix O3) display the existence of local pairs because all of them are characterized by the poor conductivity and narrow bands being the result of the strong coupling between phonons and electrons [14, 16, 17]

Summary

Introduction

For last decades there has been much progress in the discovery of new phenomena in solid state physics. There is a multitude of them, for example, Ti4O7, NaxV2O5 or CsSbCl6 and TlF2, which are not superconductors, but their ground state is charged-ordered Besides some superconductors such as A15, C15, V3Si, Nb3Ge and cuprates such as the tungsten bronzes and the doped bismuthates (Ba1−x KxBiO3 and BaPb1−x Bix O3) display the existence of local pairs because all of them are characterized by the poor conductivity and narrow bands being the result of the strong coupling between phonons and electrons [14, 16, 17]. The single-electron hopping in the narrower band was not taken into account in [15,16,17] in contrast to the Coulomb repulsion in this band which was taken exactly into account This interaction turns out to be an obstacle to get higher critical temperatures, which is in agreement with our expectations and with results obtained in [16, 17]. As is known these materials display strong coupling between phonons and electrons because they are very bad conductors in the normal state and antiferromagnetic Mott insulators when undoped [11]

The Model

The Free Energy and the Gap Equations

De e Ud and leads to the higher critical temperature than the pure

The Effect of Two Kinds of Hopping

Conclusions