Phenomenological Models of Holographic Superconductors and Hall currents

TL;DR

This paper develops a broad class of holographic superconductor models with customizable features, analyzing phase transitions, critical exponents, and Hall effects without magnetic fields, providing analytical insights and potential applications.

Contribution

It introduces a general framework for holographic superconductors with arbitrary functions, analyzing phase transitions, critical exponents, and Hall effects, expanding the modeling capabilities beyond previous specific models.

Findings

Models can exhibit first, second, and third order phase transitions.

Analytical expressions for critical exponents satisfy the Rushbrooke identity.

Hall effect can be realized without magnetic fields through a generalized theta term.

Abstract

We study general models of holographic superconductivity parametrized by four arbitrary functions of a neutral scalar field of the bulk theory. The models can accommodate several features of real superconductors, like arbitrary critical temperatures and critical exponents in a certain range, and perhaps impurities, boundary or thickness effects. We find analytical expressions for the critical exponents of the general model and show that they satisfy the Rushbrooke identity. An important subclass of models exhibits second order phase transitions. A study of the specific heat shows that general models can also describe holographic superconductors undergoing first, second and third (or higher) order phase transitions. We discuss how small deformations of the HHH model lead to the appearance of resonance peaks in the conductivity, which become narrower as the temperature is gradually decreased, without the need for tuning mass of the scalar to be close to the Breitenlohner-Freedman bound. Finally, we investigate the inclusion of a generalized "theta term" producing Hall effect without magnetic field.