Ginzburg-Landau Approach to Holographic Superconductivity

Abstract

We construct a family of minimal phenomenological models for holographic superconductors in d = 4 + 1 AdS spacetime and study the effect of scalar and gauge field fluctuations. By making a Ginzburg-Landau interpretation of the dual field theory, we determine through holographic techniques a phenomenological Ginzburg-Landau Lagrangian and the temperature dependence of physical quantities in the superconducting phase. We obtain insight on the behaviour of the Ginzburg-Landau parameter and whether the systems behaves as a Type I or Type II superconductor. Finally, we apply a constant external magnetic field in a perturbative approach following previous work by D'Hoker and Kraus, and obtain droplet solutions which signal the appearance of the Meissner effect.

Ginzburg-Landau effective action for a fluctuating holographic superconductor

“…Over the past decade or so, the holographic superconductor model has been examined in various aspects, see review papers or textbooks [25][26][27][28][29][30][31] and references therein. Interestingly, the Ginzburg-Landau free energy density (1.3) was derived in [32,33], confirming the phase transition is of second order nature; the spectrum of the Goldstone mode associated with spontaneously breaking of U (1) symmetry was identified in [34] through bulk fluctuation analysis in pure AdS.…”

Ginzburg-Landau effective action for a fluctuating holographic superconductor

“…Over the past decade or so, the holographic superconductor model has been examined in various aspects, see review papers or textbooks [25][26][27][28][29][30][31][32] and references therein. Interestingly, the Ginzburg-Landau free energy density (1.3) was derived in [33,34], 1 confirming the phase transition is of second order nature; the spectrum of the Goldstone mode associated with spontaneously breaking of U(1) symmetry was identified in [36] through bulk fluctuation analysis in pure AdS.…”

Order parameter fluctuations in the holographic superconductor

“…Furthermore, Refs. [16] and [17] study the poles of the static correlation function of the order parameter and find nontrivial poles in the complex k-plane. Since the static correlation function always has a pole at k = 0 as well, this does not contradict the fact that we find no massive modes [40].…”

“…This number density is determined from the bulk solution using Eq. (17). Notice that for a given q and m 2 , the ratio n(0)/µ 3 is fixed.…”

“…We therefore study the properties of the holographic superconductor in detail in this paper, focussing in particular on the intrinsic dynamics of the order parameter fluctuations in the normal as well as the superconducting phase. While previous studies on the order parameter dynamics mostly concentrate on the poles arXiv:1511.05112v4 [hep-th] 16 Jan 2017 of the full retarded Green's function [16,17], e.g. by finding the quasinormal modes [18], we directly calculate the intrinsic two-point correlation function of the order parameter, using scalar field fluctuations in the gravity theory.…”