Holographic Superconductors with Ho\v{r}ava-Lifshitz Black Holes

TL;DR

This paper investigates holographic superconductors within Hořava-Lifshitz black holes, analyzing phase transitions, condensates, and conductivity, revealing robustness of holographic superconductivity akin to Schwarzschild-AdS black holes.

Contribution

It introduces a study of holographic superconductors in Hořava-Lifshitz gravity, highlighting phase transition behavior and conductivity features similar to AdS black holes.

Findings

Existence of condensates for specific scalar masses.

Presence of a conductivity spike for certain operator dimensions.

Holographic superconductivity shows robustness across different black hole backgrounds.

Abstract

We discuss the phase transition of planar black holes in Ho\v{r}ava-Lifshitz gravity by introducing a Maxwell field and a complex scalar field. We calculate the condensates of the charged operators in the dual CFTs when the mass square of the complex scalar filed is $m^2=-2/L^2$ and $m^2=0$, respectively. We compute the electrical conductivity of the \hl superconductor in the probe approximation. In particular, it is found that there exists a spike in the conductivity for the case of the operator with scaling dimension one. These results are quite similar to those in the case of Schwarzschild-AdS black holes, which demonstrates that the holographic superconductivity is a robust phenomenon associated with asymptotic AdS black holes.