Superconducting transition-temperature enhancement due to electronic-band-structure density-of-states

Abstract

We briefly review a simple statistical model of a boson-fermion mixture of unpaired fermions plus linear-dispersion-relation Cooper pairs that leads to Bose-Einstein condensation (BEC) for all dimensions greater than unity. (The "dispersion relation" of a particle is its energy vs. momentum relation.) This contrasts sharply with "ordinary" BEC for a many-boson assembly of non-interacting bosons each moving in vacuum with a quadratic dispersion relation, which is well-known to occur only for dimensions greater than two. The BEC critical temperatures T-c are substantially higher than those of the BCS theory of superconductivity, for the same BCS model interaction between the fermions that gives rise to the Cooper pairs, at both weak and strong couplings. However, these results hold with an ideal-fermi-gas (IFG) density-of-states (DOS) for the underlying electron (or hole) carriers. We then show that even higher T-c values are obtained in 2D if a non-IFG DOS is employed which reflects the electronic band structure of the quasi-2D copper-oxygen planes characteristic of cuprate superconductors. The non-IFG DOS used are both a so-called Van Hove scenario (VHS) with a logarithmic singularity in the DOS, and a DOS with a power-law-singularity associated with an extended-saddle-point (ESP) in the energy-momentum curve.