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

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.

v1: 24 pages, 9 figures; v2: presentation improved

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