Upper bound on the specific-heat jump: Application to the high-Tcoxides

Abstract

We establish an upper limit on the normalized specific-heat jump $\frac{\Delta C}{\gamma \mathrm{}\left(0\right)\mathrm{}{T}_c}$ at $T_c$, for the case of an isotropic Eliashberg superconductor. Functional derivative results for $\frac{\Delta C}{\gamma \mathrm{}\left(0\right)\mathrm{}{T}_c}$, in the case of realistic electron-phonon spectral densities, lead us to consider a model delta-function spectrum which, we can prove, gives a local maximum in $\frac{\Delta C}{\gamma \mathrm{}\left(0\right)\mathrm{}{T}_c}$ for some low but finite phonon energy. The value of the maximum depends somewhat on the value of Coulomb pseudopotential (${\mu }^{*}$) used, but is always surprisingly small. As an example for ${\mu }^{*}=0.15\mathrm{}$, $\frac{\Delta C}{\gamma \mathrm{}\left(0\right)\mathrm{}{T}_c}\le 3.73$ with the inequality holding for realistic spectra. This is smaller than some recent experimental values published for ${\mathrm{La}}_{1.85}$ ${\mathrm{Sr}}_{0.15}$Cu${\mathrm{O}}_4$.