Holographic superconductors with Hořava-Lifshitz black holes

Abstract

We discuss the phase transition of planar black holes in Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity by introducing a Maxwell field and a complex scalar field. We calculate the condensate of the charged operators in the dual conformal field theories when the mass square of the complex scalar field is ${m}^{2}=\ensuremath{-}2/{L}^{2}$ and ${m}^{2}=0$, respectively. We compute the electrical conductivity of the Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz 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.