Fluctuation contribution to the specific heat in non-Fermi models for superconductivity

Abstract

We investigate the fluctuation contribution to the specific heat of a two-dimensional superconductor with a non-Fermi normal state described by a Anderson Green's function $G(k,iω)=ω_c^{-α}/(iω-ε_k)^{1-α}$. The specific heat corrections contain a term proportional to $(T^{2α-T_c^{2α}})^{-1}$ and another logarithmic one. We defined a coherence length as function of the non-Fermi parameter $α$, which showed that a crossover study between BCS and Bose-Einstein condensation is possible by varying $α$ in an interval $0 ÷α_{cr}$. By comparing our theoretical results with the experimental data for HTSC materials, we reobtained the value for $α$, corresponding to such systems, of the order $0.3 ÷0.45$. We also reobtained the critical temperature for such a superconductor using the Thouless criterion.