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Possible Anderson localization in a holographic superconductor

We study the effect of disorder in a holographic superconductor by introducing a quasi-periodic chemical potential. When the condensation of the superconductor is sufficiently small compared with the strength of disorder, we find that there exists a discontinuous phase transition from superconducting state to normal state with increasing disorder strength. For relatively large condensation, we find that disorder suppress but not completely destroy superconductivity. This model may provide a holographic realization of Anderson Localization in two-dimensional superconductor.