Flow Equation and Fermion Gap in the Holographic Superconductors

TL;DR

This paper analyzes the fermion spectral function in holographic superconductors, deriving a matrix Riccati equation for precise calculations, and compares results with BCS theory across different densities.

Contribution

It introduces a matrix Riccati equation approach to compute fermion spectral functions in holographic superconductors, incorporating the effects of scalar-fermion interactions and density variations.

Findings

The spectral gap structure aligns with s-wave superconductor expectations.

Results match BCS theory at low chemical potential.

High-density cases show significant deviations from BCS predictions.

Abstract

We reconsider the fermion spectral function in the presence of the Cooper pair condensation and identified the interaction type of complex scalar and fermion, which gives consistent results with the expected s-wave superconductor for the first time. We derive the matrix Riccati equation, which allows the precise calculation of the fermion spectral function. Apart from the gap structure, we studied the effect of the chemical potential and the density and compared it with the BCS theory. We found that two theories give similar results in small chemical potential but very different ones in the high-density case, which we attribute to the correlation effect.