Heun's equation and analytic structure of the Gap in Holographic superconductivity

Abstract

We analytically calculate physical observables of holographic superconductor including the critical temperature and the condensation as functions of ρ, T, ∆, which are density, temperature and the scaling dimension of the Cooper pair operator respectively. In two spatial dimension, e.g, the critical temperature has the power law dependence on the coupling, T c ∼ (gρ) 1/2 , which can be much higher than the exponential suppression in the BCS theory, T c ∼ exp(−C/g) for small g.

Momentum dependent gap in holographic superconductors revisited

“…The gauge/gravity duality [1]- [4] has been applied to strongly correlated systems as an efficient tool to handle the strong coupling. In the context of this duality, a theory of superconductivity was set up [5] using the spontaneous symmetry breaking of the U (1) symmetry of an Abelian Higgs model coupled to AdS the gravity [6], [7], after which huge number of investigations on s-wave holographic superconductors [12]- [22] has been reported in past decade. Although the original model [5] allowed to estimate the gap and the critical temperature of conductivity of isotropic system, typical high T c superconductors show the momentum dependent gap structure ∆ k [8,9,11] which has been considered as one of the most important finger prints of high T c superconductors.…”

Flow Equation and Fermion Gap in the Holographic Superconductors

“…Understanding the high Tc superconductivity has been one of the major motivations to study strongly correlated systems. Therefore there have been huge activities for holographic superconductivity [1][2][3][4][5][6][7][8][9][10][11][12] based on the gauge gravity duality [13][14][15][16]. The novel achievement was to construct a new dynamical mechanism of the instability to give the U(1) symmetry breaking from the dynamics of the scalar-vector-gravity system [1,2].…”