Homes' law in holographic superconductor with linear-$T$ resistivity

TL;DR

This paper explores how Homes' law, a universal relation in superconductors, can be realized in holographic models that exhibit linear-temperature resistivity, emphasizing the role of momentum relaxation.

Contribution

It demonstrates that strong momentum relaxation is crucial for realizing Homes' law alongside linear-$T$ resistivity in holographic superconductor models.

Findings

Homes' law can be achieved with linear-$T$ resistivity in holographic models.

Strong momentum relaxation is essential for this realization.

The study connects holographic models with experimental observations in high-$T_c$ superconductors.

Abstract

Homes' law, $\rho_{s} = C \, \sigma_{DC} \, T_{c}$, is a universal relation of superconductors between the superfluid density $\rho_{s}$ at zero temperature, the critical temperature $T_{c}$ and the electric DC conductivity $\sigma_{DC}$ at $T_c$. Experimentally, Homes' law is observed in high $T_c$ superconductors with linear-$T$ resistivity in the normal phase, giving a material independent universal constant $C$. By using holographic models related to the Gubser-Rocha model, we investigate how Homes' law can be realized together with linear-$T$ resistivity in the presence of momentum relaxation. We find that strong momentum relaxation plays an important role to exhibit Homes' law with linear-$T$ resistivity.