Holographic $s$-wave superconductors with conformal anomaly correction

TL;DR

This paper investigates how conformal anomaly correction affects holographic s-wave superconductors and insulators, revealing that increasing the CAC parameter enhances phase transition tendencies and alters energy gaps.

Contribution

It introduces a conformal anomaly corrected holographic superconductor model and analyzes the impact of CAC parameter on phase transitions and energy gaps.

Findings

Critical temperature increases with CAC parameter in conductor/superconductor model.

Critical chemical potential decreases with CAC parameter in insulator/superconductor model.

Energy gap decreases monotonically as CAC parameter increases.

Abstract

We build a holographic $s$-wave conductor/superconductor model and an insulator/superconductor model in the four-dimensional conformal anomaly corrected~(CAC) AdS gravity. The effects of CAC parameter $\alpha$ are studied using both numerical and analytical methods in the probe approximation. Concretely, when the CAC parameter increases, the critical temperature increases for the conductor/superconductor phase transition, while the critical chemical potential decreases for the insulator/superconductor case, which suggests that the increasing CAC parameter enhances both superconducting phase transitions. Meanwhile, below the critical temperature or beyond the critical chemical potential, the scalar hair begins to condense, and the condensed phases are found to be thermodynamically stable. The critical behaviors obtained from numerics are confirmed by our analytical analysis. For the parameters we are considering, the energy gap in the conductor/superconductor model decreases monotonically by increasing the CAC parameter, while for the insulator/superconductor model the energy of quasiparticle excitations decreases with the CAC parameter.