Momentum dependent gap in holographic superconductors revisited

TL;DR

This paper investigates the angular dependence of the gap structure in holographic superconductors, clarifying the nature of s-wave and p-wave states, and proposing a modified ansatz to explore complex order parameters.

Contribution

It provides a detailed analysis of the gap structure in vector and scalar holographic superconductor models, including a new ansatz for p_x ± ip_y order parameters.

Findings

Normalizable ground state is p-wave in vector model.

Ground state is s-wave in scalar model.

Critical temperature is higher in vector model for fixed conformal dimension.

Abstract

We reconsider the angular dependence in gap structure of holographic superconductors, which has not been treated carefully so far. For the vector field model, we show that the normalizable ground state is in the p-wave state because s-wave state is not normalizable. On the other hand, in the scalar order model, the ground state is in the $s$-wave. The angle dependent gap function is explicitly constructed in these models. We also suggest the modified ansatz of the vector order which enables to discuss the order $p_{x}\pm ip_{y}$ gap, which has not been possible so far. We have also analytically investigated the critical temperature and the behavior of the gap near there. Interestingly, for the fixed conformal dimension of the Cooper pair operator, the critical temperature in vector model is higher than that of the scalar model.