# A simple holographic superconductor with momentum relaxation

Journal of High Energy Physics, Apr 2015

We study a holographic superconductor model with momentum relaxation due to massless scalar fields linear to spatial coordinates(ψ I = βδ Ii 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 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($\overline{\kappa}$) conductivities. When the system undergoes a phase transition from 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 $\overline{\kappa}$, 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.

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Keun-Young Kim, Kyung Kiu Kim, Miok Park. A simple holographic superconductor with momentum relaxation, Journal of High Energy Physics, 2015, 152, DOI: 10.1007/JHEP04(2015)152