A Simple Holographic Superconductor with Momentum Relaxation

Keun-Young Kim; Kyung Kiu Kim; Miok Park

doi:10.1007/JHEP04(2015)152

paper

A Simple Holographic Superconductor with Momentum Relaxation

arXiv:1501.00446 · doi:10.1007/JHEP04(2015)152

Abstract

We study a holographic superconductor model with momentum relaxation due to massless scalar fields linear to spatial coordinates( $ψ_{I} = β δ_{I i} x^{i}$ ), where $β$ is the strength of momentum relaxation. In addition to the original superconductor induced by the chemical potential( $μ$ ) at $β = 0$ , there exists a new type of superconductor induced by $β$ even at $μ = 0$ . It may imply a new `pairing' mechanism of particles and antiparticles interacting with $β$ , which may be interpreted as `impurity'. Two parameters $μ$ and $β$ compete in forming a superconducting phase. As a result, the critical temperature behaves differently depending on $β / μ$ . It decreases when $β / μ$ is small and increases when $β / μ$ is large, which is a novel feature compared to other models. After analysing ground states and phase diagrams for various $β / μ$ , we study optical electric( $σ$ ), thermoelectric( $α$ ), and thermal( $κ ˉ$ ) conductivities. When the system undergoes a phase transition from a normal to a superconducting phase, $1/ ω$ pole appears in the imaginary part of the electric conductivity, implying infinite DC conductivity. If $β / μ < 1$ , at small $ω$ , a two-fluid model with an imaginary $1/ ω$ pole and the Drude peak works for $σ$ , $α$ , and $κ ˉ$ , but if $β / μ > 1$ 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 $μ = 0$ .

v3: Minor chages, version accepted in JHEP

A Simple Holographic Superconductor with Momentum Relaxation

Abstract

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