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

We briefly review a simple statistical model of a boson-fermion mixture of unpaired fermions plus linear-dispersion-relation Cooper pairs that leads t o 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 re lation, which is well-known to occur only for dimensions greater than two. The BEC critical temperatures T-c are substantially higher than those of th e BCS theory of superconductivity, for the same BCS model interaction betwe en the fermions that gives rise to the Cooper pairs, at both weak and stron g couplings. However, these results hold with an ideal-fermi-gas (IFG) dens ity-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 em ployed which reflects the electronic band structure of the quasi-2D copper- oxygen planes characteristic of cuprate superconductors. The non-IFG DOS us ed are both a so-called Van Hove scenario (VHS) with a logarithmic singular ity in the DOS, and a DOS with a power-law-singularity associated with an e xtended-saddle-point (ESP) in the energy-momentum curve.