Holographic p-wave Superconductor with Disorder

Abstract

We implement the effects of disorder on a holographic p-wave superconductor by introducing a random chemical potential which defines the local energy of the charge carriers. Since there are various possibilities for the orientation of the vector order parameter, we explore the behavior of the condensate in the parallel and perpendicular directions to the introduced disorder. We clarify the nature of various branches representing competing solutions and construct the disordered phase diagram. We find that moderate disorder enhances superconductivity as determined by the value of the condensate. Though we mostly focus on uncorrelated noise, we also consider a disorder characterized by its spectral properties and study in detail its influence on the spectral properties of the condensate and charge density. We find fairly universal responses of the resulting power spectra characterized by linear functions of the disorder power spectrum.

30 pages, 12 figures. v2: References added, typos corrected. v3: Extended discussion of the characteristics of the noise, new sections focused on uncorrelated noise. v4: minor typos corrected, JHEP version

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• The Holographic Disorder-Driven Superconductor-Metal Transition
• Thermal conductivity at a disordered quantum critical point
• On the stability of soliton and hairy black hole solutions of $\mathfrak{su}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant
• On the stability of dyons and dyonic black holes in Einstein-Yang-Mills theory
• Conductivity bound from dirty black holes
• Marginal and Irrelevant Disorder in Einstein-Maxwell backgrounds
• Coherence effects in disordered geometries with a field-theory dual
• Disorder-dependent superconducting pairing symmetry in doped graphene
• Noisy Branes
• Disorder in AdS${}_3$/CFT${}_2$