Optical properties of Born-Infeld-dilaton-Lifshitz holographic superconductors

TL;DR

This paper investigates the optical properties of Lifshitz-dilaton holographic superconductors with nonlinear Born-Infeld electrodynamics, revealing how anisotropy and nonlinearity affect critical temperature and demonstrating metamaterial behavior in certain low-dimensional cases.

Contribution

It introduces a detailed analysis of Lifshitz-dilaton holographic superconductors with nonlinear Born-Infeld fields, highlighting the impact of anisotropy and nonlinearity on phase transition and optical properties.

Findings

Critical temperature decreases with increasing Lifshitz exponent and nonlinearity.

Low-frequency metamaterial behavior observed in (2+1)-dimensional case.

No metamaterial behavior in (3+1)-dimensional case.

Abstract

In this paper, we first study the Lifshitz-dilaton holographic superconductors with nonlinear Born-Infeld (BI) gauge field and obtain the critical temperature of the system for different values of Lifshitz dynamical exponent, $z$, and nonlinear parameter $b$. We find that for fixed value of $b$, the critical temperature decreases with increasing $z$. This indicates that the increase of anisotropy between space and time prevents the phase transition. Also, for fixed value of $z$, the critical temperature decrease with increasing $b$. Then, we investigate the optical properties of ($2+1$) and ($3+1$)-dimensional BI-Lifshitz holographic superconductors in the the presence of dilaton field. We explore the refractive index of the system. For $z=1$ and $(2+1)$-dimensional holographic superconductor, we observe negative real part for permittivity $\textrm{Re}[\epsilon]$ as frequency $\omega $ decreases. Thus, in low frequency region our superconductor exhibit metamaterial property. This behaviour is independent of the nonlinear parameter and can be seen for either linear ($b=0$) and nonlinear ($b\neq 0$) electrodynamics. Interestingly, for ($3+1$)-dimensional Lifshitz-dilaton holographic superconductors, we observe metamaterial behavior neither in the presence of linear nor nonlinear electrodynamics.