Generalising Holographic Superconductors

Abstract: In this paper we propose a generalised holographic framework to describe superconductors. We first unify the description of s-, p- and d-wave superconductors in a way that can be easily promoted to higher spin. Using a semi-analytical procedure to compute the superconductor properties, we are able to further generalise the geometric description of the hologram beyond the AdS-Schwarzschild Black Hole paradigm, and propose a set of higher-dimensional metrics which exhibit the same universal behaviour. We then study the properties of the condensate and the scaling of the critical temperature with the parameters of the higher-dimensional theory, reproducing existing results in the literature and extending them to include a possible description of the newly observed f-wave superconducting systems.