Bose-Einstein Gas Model for T_c and Energy Gap for Most Superconductors, Especially the Ceramic Oxides

Abstract

A generalized Bose-Einstein gas model is sufficient to derive reasonable estimates of T_c, the energy gap, and the coherence length for all classes of superconductors such as the ceramic oxides, the metairics, heavy-fermion metals, metallic hydrogen, and neutron stars for 3-dimensional, quasi-2 and quasi-1 dimensional states. Analysis of the new high-temperature ceramic oxide superconductors determines upper limits of T_c using as input the number density of conduction electrons and the effective mass of the charge carriers. This calculation for the ceramic oxides yields 10K, 40K, and 300K in 3, Q2, and Ql dimensions. Interpreting the ceramic oxide case as one in which the interchain interactions are equal to the intrachain interactions, leads to

$$ {{\text{T}}_{\text{c}}}{\text{ = (}}{{\text{T}}_{{\text{c1}}}}{{\text{T}}_{{\text{c2}}}}{{\text{)}}^{{\text{1/2}}}}{\text{ = }}{({\text{300K}} \times {\text{40K)}}^{{\text{1/2}}}}{\text{ = 110K = 100K}} $$

as the approximate transition temperature for these materials when there is clearly a combined linear and planar structure. It is noteworthy that without specifying a coupling mechanism or coupling strength, this general model does well in calculating transition temperatures, and coupling strengths over nine orders of magnitude (1K to 10⁹K and meV to MeV) from the heavy fermion metals to neutron stars.