Holographic Superconductor/Insulator Transition with logarithmic electromagnetic field in Gauss-Bonnet gravity

TL;DR

This paper investigates holographic superconductor/insulator transitions within Einstein-Gauss-Bonnet gravity, revealing how logarithmic electromagnetic fields influence phase transitions, critical parameters, and conductivity properties.

Contribution

It introduces a charged scalar coupled with a logarithmic electromagnetic field in Gauss-Bonnet gravity, analyzing effects on phase transitions and conductivity in holographic models.

Findings

Larger logarithmic coupling $b$ facilitates scalar hair condensation.

The ratio $rac{ ext{gap frequency}}{T_c}$ depends on $b$ and $\alpha$.

Critical exponents are unaffected by $b$ and $\alpha$.

Abstract

The behaviors of the holographic superconductors/insulator transition are studied by introducing a charged scalar field coupled with a logarithmic electromagnetic field in both the Einstein-Gauss-Bonnet AdS black hole and soliton. For the Einstein-Gauss-Bonnet AdS black hole, we find that: i) the larger coupling parameter of logarithmic electrodynamic field $b$ makes it easier for the scalar hair to be condensated; ii) the ratio of the gap frequency in conductivity $\omega_g$ to the critical temperature $T_c$ depends on both $b$ and the Gauss-Bonnet constant $\alpha$; and iii) the critical exponents are independent of the $b$ and $\alpha$. For the Einstein-Gauss-Bonnet AdS Soliton, we show that the system is the insulator phase when the chemical potential $\mu$ is small, but there is a phase transition and the AdS soliton reaches the superconductor (or superfluid) phase when $\mu$ larger than critical chemical potential. A special property should be noted is that the critical chemical potential is not changed by the coupling parameter $b$ but depends on $\alpha$.