Holographic conductivity of holographic superconductors with higher order corrections

TL;DR

This paper investigates how higher order curvature and gauge field corrections influence the properties of s-wave holographic superconductors, revealing that nonlinearity makes condensation more difficult and affects the conductivity spectrum.

Contribution

It provides an analytical and numerical analysis of higher order corrections in holographic superconductors, including effects on critical temperature, condensation, and conductivity.

Findings

Critical temperature decreases with gauge field nonlinearity.

Nonlinear corrections hinder the condensation process.

Conductivity spectra are affected by higher order parameters, showing shifts in the imaginary part's minimum.

Abstract

We analytically as well as numerically disclose the effects of the higher order correction terms in the gravity and in the gauge field on the properties of $s$-wave holographic superconductors. On the gravity side, we consider the higher curvature Gauss-Bonnet corrections and on the gauge field side, we add a quadratic correction term to the Maxwell Lagrangian. We show that for this system, one can still obtain an analytical relation between the critical temperature and the charge density. We also calculate the critical exponent and the condensation value both analytically and numerically. We use a variational method, based on the Sturm-Liouville eigenvalue problem for our analytical study, as well as a numerical shooting method in order to compare with our analytical results. For a fixed value of the Gauss-Bonnet parameter, we observe that the critical temperature decreases with increasing the nonlinearity of the gauge field. This implies that the nonlinear correction term to the Maxwell electrodynamics make the condensation harder. We also study the holographic conductivity of the system and disclose the effects of Gauss-Bonnet and nonlinear parameters $\alpha$ and $b$ on the superconducting gap. We observe that for various values of $\alpha $ and $b$, the real part of conductivity is proportional to the frequency per temperature, $\omega /T$, as frequency is enough large. Besides, the conductivity has a minimum in the imaginary part which is shifted toward greater frequency with decreasing the temperature.