Homes’ law in holographic superconductor with linear-T resistivity

Abstract Homes’ law, ρ s = Cσ DC T c , is a universal relation of superconductors between the superfluid density ρ s at zero temperature, the critical temperature T c and the electric DC conductivity σ 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.