Analysis of s-wave, p-wave and d-wave holographic superconductors in Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper investigates s-wave, p-wave, and d-wave holographic superconductors within Hořava-Lifshitz gravity, revealing unified equations, numerical properties of condensates and conductivities, and comparing critical temperatures to Einstein gravity.

Contribution

It extends the analysis of holographic superconductors to Hořava-Lifshitz gravity, deriving a unified framework and exploring how parameters affect condensation and critical temperatures.

Findings

Condensates form in all three wave states in Hořava-Lifshitz gravity.

Certain parameters yield identical condensation curves to Einstein gravity.

Non-zero α facilitates condensation in s-wave superconductors.

Abstract

In this work, the s-wave, p-wave and d-wave holographic superconductors in the Ho\v{r}ava-Lifshitz gravity are investigated in the probe limit. For the present approach, it is shown that the equations of motion for different wave states in Einstein gravity can be written into a unified form, and condensates take place in all three cases. This scheme is then generalized to Ho\v{r}ava-Lifshitz gravity, and an unified equation for multiple holographic states is obtained. Furthermore, the properties of the condensation and the optical conductivity are studied numerically. It is found that, in the case of Ho\v{r}ava-Lifshitz gravity, it is always possible to find some particular parameters in the corresponding Einstein case where the condensation curves are identical. For fixed scalar field mass $m$, a non-vanishing $\alpha$ becomes the condensation easier than in Einstein gravity for s-wave superconductor. However, the p-wave and d-wave superconductors have $T_c$ greater than s-wave one.