Zero temperature limit of holographic superconductors

Abstract

We consider holographic superconductors whose bulk description consists of gravity minimally coupled to a Maxwell field and charged scalar field with general potential. We give an analytic argument that there is no "hard gap": the real part of the conductivity at low frequency remains nonzero (although typically exponentially small) even at zero temperature. We also numerically construct the gravitational dual of the ground state of some holographic superconductors. Depending on the charge and dimension of the condensate, the infrared theory can have emergent conformal or just Poincare symmetry. In all cases studied, the area of the horizon of the dual black hole goes to zero in the extremal limit, consistent with a nondegenerate ground state.1 Some early indications of emergent Poincare symmetry were found in [13]

Competition/enhancement of two probe order parameters in the unbalanced holographic superconductor

“…The instability leading to scalar hair formation is associated to the violation of the Breitenlohner-Freedman bound for a scalar field living on the near-horizon AdS 2 geometry [15]. The study of the near horizon geometry of the doubly charged Reissner-Nordström black hole solution at T = 0 leads to the following condition for instability 6…”

“…An analogous approach appears to be not feasible here. In principle a similar near-horizon analysis could be performed, but here we encounter a problem: actually we would like to study one scalar on a hairy black hole background (namely on a solution where the other, say λ, scalar has already undergone condensation); even though we have an analytical expression for the fields of the hairy black hole in the IR region [15], on such background the equation for ψ fluctuations does not reduce to a simple free scalar on an AdS spacetime. In other words, here we cannot just apply a simple BF bound argument to study IR stability.…”

“…One could worry about the stability of the scalar potential and particularly about the fact that it could be unbounded from below. However, we work in a probe approximation where the fields are regarded as small fluctuations; consequently, our effective model can be thought of to be corrected by higher order terms in the potential which nevertheless 12 See [15] for the analogous study in the balanced case.…”

Holography of charged dilaton black holes in general dimensions

“…A useful formulation was proposed in [17], which stated that after introducing a perturbative gauge field A x (r, t), the corresponding equation of motion for A x could be recast in a Schrödinger-like form…”

“…It has been pointed out in [17] that such a formulation could be generalized to higherdimensional cases.…”