Holographic superconductor in the exact hairy black hole

TL;DR

This paper explores a holographic superconductor model using a charged hairy black hole, analyzing phase transitions and condensate behavior, with findings indicating charge effects suppress condensates at low temperatures.

Contribution

It introduces an analytic model of a holographic superconductor based on the CMTZ black hole and examines phase transition dynamics and condensate suppression due to charge.

Findings

Phase transition between CMTZ and HRNAdS black holes is unlikely.

Charge destroys condensates near zero temperature.

Thermodynamic analysis supports condensate suppression by charge.

Abstract

We study the charged black hole of hyperbolic horizon with scalar hair (charged Martinez-Troncoso-Zanelli: CMTZ black hole) as a model of analytic hairy black hole for holographic superconductor. For this purpose, we investigate the second order phase transition between CMTZ and hyperbolic Reissner-Nordstr\"om-AdS (HRNAdS) black holes. However, this transition unlikely occur. As an analytic treatment for holographic superconductor, we develop superconductor in the bulk and superfluidity on the boundary using the CMTZ black hole below the critical temperature. The presence of charge destroys the condensates around the zero temperature, which is in accord with the thermodynamic analysis of the CMTZ black hole.