A simple holographic superconductor with momentum relaxation

Abstract

We study a holographic superconductor model with momentum relaxation due to massless scalar fields linear to spatial coordinates(psi(I) = beta delta(Ii)x(i)), where beta is the strength of momentum relaxation. In addition to the original superconductor induced by the chemical potential(mu) at beta = 0, there exists a new type of superconductor induced by beta even at mu = 0. It may imply a new &apos;pairing&apos; mechanism of particles and antiparticles interacting with beta, which may be interpreted as &apos;impurity&apos;. Two parameters mu and beta compete in forming superconducting phase. As a result, the critical temperature behaves differently depending on beta/mu. It decreases when beta/mu is small and increases when beta/mu is large, which is a novel feature compared to other models. After analysing ground states and phase diagrams for various beta/mu, we study optical electric(sigma), thermoelectric(alpha), and thermal((kappa) over bar) conductivities. When the system undergoes a phase transition from normal to a superconducting phase, 1/omega pole appears in the imaginary part of the electric conductivity, implying infinite DC conductivity. If beta/mu < 1, at small omega, a two-fluid model with an imaginary 1/omega pole and the Drude peak works for sigma, alpha, and <(kappa)over bar>, but If beta mu > 1 a non-Drude peak replaces the Drude peak. It is consistent with the coherent/incoherent metal transition in its metal phase. The Ferrell-Glover-Tinkham (FGT) sum rule is satisfied for all cases even when mu = 0.