Theoretical, Materials and Condensed Matter Physics

Biography

Biography: I Chávez

Abstract

The generalized Bose-Einstein condensation (GBEC) theory subsumes as special cases both BCS and BEC, among other theories. It hinges on three separate new ingredients: i) treating Cooper pairs (CPs) as actual bosons as distinct from BCS pairs which strictly speaking are not bosons; ii) inclusion of two-hole Cooper pairs (2hCPs) on an equal footing with the usual two-electron ones (2eCPs); and iii) incorporating in the resulting ideal ternary boson-fermion (BF) gas specific vertex interactions that drive formation/dis-integration processes of both kinds of CPs. Here we extend the BCS-Bose crossover theory by explicitly including 2hCPs. This leads to a phase diagram with two pure phases, one with 2eCPs and the other with 2hCPs, plus a mixed phase with arbitrary proportions of both. The special-case phase with a 50-50 mixture of both 2e/2hCPs gives the usual unextended BCS-Bose crossover theory. Furthermore, if Tc and TF are respectively the critical and the Fermi temperatures, it predicts Tc /TF values for the elemental superconductors Al, In, Sn, Pb, Hg, and Nb comparing quite well with experiment and notably much better than BCS predictions. Also shown is a phase diagram of the dimensionless energy gap at zero-temperature Δ(0)/EF vs n/nf , where EF =kB TF is the Fermi energy. We do this for the 50-50 case as well as for the pure 2eCPs and 2hCPs cases separately. It is thus unequivocally shown that if one ignores 2hCPs the energy gap lies substantially below the 50-50 case which already roughly reproduces the data.