Scaling behavior of superconductors

TL;DR

This paper reviews the universal scaling properties of superconductors, demonstrating that certain laws like Homes' law apply broadly, and supports the theory that fermion condensation is fundamental to superconductor physics.

Contribution

It provides a unified analysis of experimental data and theoretical explanation showing the universality of scaling laws and the role of fermion condensation in both conventional and unconventional superconductors.

Findings

Homes' law applies to both high-$T_c$ and ordinary superconductors

Scaling relationships reveal fundamental laws of superconductor physics

Fermion condensation quantum phase transition explains key properties

Abstract

In our brief review, we will consider the general universal scaling properties of superconductors. The physics of superconductors, represented by both conventional and unconventional superconductors, has been the main topic of high-$T_c$ superconductor physics for over thirty years, revealing some of the properties of high-$T_c$ (or unconventional) superconductors. Scaling relationships lead to the identification of fundamental laws of nature and reveal the essence of superconductor physics. Advances in experimental technology allow us to collect important data, which in turn allow us to make definitive statements about the physical processes underlying strongly correlated Fermi systems. 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 $\rho_{s0}= (1/2\pi\lambda_D)^2= T_c\sigma(T_c)$ is applicable to the both types of superconductors. Here $\rho_{s0}$ is the superconducting electron density, $\lambda_D$ is the zero-$T$ penetration depth, $\sigma$ is the normal state conductivity, $T$ is temperature and $T_c$ is the temperature of superconducting phase transition. Overall, these scaling relationships lead to the identification of fundamental laws of nature and reveal the essence of superconductor physics. All these observations support the theory of fermion condensation. Our theoretical results agree well with a body of diverse and seemingly unrelated experimental facts. They show that the topological fermion condensation quantum phase transition, generating flat bands, is an intrinsic property of strongly correlated Fermi systems and can be considered as a universal agent explaining their basic physics.