General Scaling Behavior of Superconductors

Abstract

The physics of high-Tc superconductors, which has been a major topic in condensed matter physics for more than thirty years, reveals some features of conventional superconductors. We analyze the scaling of the condensation energy divided by,, that equally applicable to both conventional and unconventional high-Tc superconductors. Here, is the density of states, is the maximum value of the superconducting gap, and is the Sommerfeld coefficient. Basing on this observation, we analyze experimental facts that reveal the general scaling properties of both high-Tc and ordinary superconductors, and theoretically explain that the Homes’ law is applicable to the both types of superconductors. Here, is the conductivity, is the temperature, Tc is the superconducting transition temperature, is the zero-T penetration depth, and is the superconducting electron density. For the first time, we also explain the reason of violation of the Homes’ law. Our theoretical results agree well with experimental facts.