JETP Letters: issues online

The physics of high-T_c 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 E_Δ divided by γ, $E_{\Delta}/\gamma\simeq N(0)\Delta_1^2/\gamma$ , that equally applicable to both conventional and unconventional high-T_c superconductors. Here N(0) is the density of states, Δ₁ is the maximum value of the superconducting gap and γ is the Sommerfeld coefficient. Basing on this observation, we analyze experimental facts that reveal the general scaling properties of both high-T_c and ordinary superconductors, and theoretically explain that the Homes' law $\rho_{s0}\propto T_c\sigma(T_c)$ is applicable to the both types of superconductors. Here σ is the conductivity, T is temperature and T_c is the temperature of superconduction phase transition, λ_D is the zero-T penetration depth, and ρ_s0 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.