Common behavior of the scaled condensation energy for both high-$T_c$ and conventional superconductors

Abstract

We analyze the scaling of the condensation energy $E_{\Delta}$ divided by $\gamma$, $E_{\Delta}/\gamma\simeq N(0)\Delta_1^2/\gamma$, of both conventional superconductors and unconventional high-$T_c$ one, where $N(0)$ is the density of states, $\Delta_1$ is the maximum value of the superconducting gap and $\gamma$ is the Sommerfeld coefficient. For the first time, we show that the universal scaling of $E_{\Delta}/\gamma\propto T_c^2$ applies equally to conventional superconductors and unconventional high-$T_c$ ones. Our consideration is based on both facts: Bogoliubov quasiparticles act in conventional and unconventional superconductors, and the corresponding flat band is deformed by the unconventional superconducting state. As a result, our theoretical observations based on the fermion condensation theory are in good agreement with experimental facts.