On Some Factors Affecting the Critical Temperature in a Two-Band Model of Superconductivity
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O R I G I N A L PA P E R
On Some Factors Affecting the Critical Temperature in a Two-Band Model of Superconductivity P. Tarasewicz
Received: 13 October 2012 / Accepted: 15 March 2013 © The Author(s) 2013. This article is published with open access at Springerlink.com
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. Keywords Superconductivity · Two-band model · Fermion pairs · Critical temperature
P. Tarasewicz () Faculty of Pharmacy, Collegium Medicum, Bydgoszcz Nicolaus Copernicus University in Toru´n, ul. Jagiello´nska 13, 85-067 Bydgoszcz, Poland e-mail: [email protected]
1 Introduction For last decades there has been much progress in the discovery of new phenomena in solid state physics. The high-temperature superconductivity or the so-called heavyfermion superconductivity belongs to this class. An especially intriguing question became the problem of mechanisms leading to such effects. The crucial question is how the critical temperature can be increased in relation to the BCS values. 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. However, in view of experimental facts such an approach seems at least insufficient. The internal structure of new superconducting materials is much more complicated than the structure of simple metals or their alloys. The conventional BCS theory based on the concept of the phonon-mediated two-electron attraction does not include this at all. That is why there have been invoked many proposals of mechanisms explaining not only higher critical temperatures but a lot of
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