Competition between the s-wave and p-wave superconductivity phases in a holographic model

TL;DR

This paper develops a holographic superconductor model featuring both s-wave and p-wave condensates, revealing a narrow temperature window where they coexist and compete, with the coexisting phase being thermodynamically favored.

Contribution

It introduces a novel holographic superconductor model with scalar triplet and SU(2) gauge field, demonstrating coexistence and competition of s-wave and p-wave phases.

Findings

Four distinct phases identified: normal, s-wave, p-wave, and s+p coexistence.

The s+p phase is thermodynamically favored when it appears.

The coexistence phase exists within a narrow temperature range.

Abstract

We build a holographic superconductor model with a scalar triplet charged under an SU(2) gauge field in the bulk. In this model, the s-wave and p-wave condensates can be consistently realized. We find that there are totally four phases in this model, namely, the normal phase without any condensate, s-wave phase, p-wave phase and the s+p coexisting phase. By calculating Gibbs free energy, the s+p coexisting phase turns out to be thermodynamically favored once it can appear. The phase diagram with the dimension of the scalar operator and temperature is drawn. The temperature range for the s+p coexisting phase is very narrow, which shows the competition between the s-wave and p-wave orders in the superconductor model.