Lifshitz scaling effects on the holographic p-wave superconductors coupled to nonlinear electrodynamics

TL;DR

This paper investigates how Lifshitz scaling influences holographic p-wave superconductors within nonlinear electrodynamics, revealing that increased nonlinearities and scaling make phase transitions harder and affect conductivity behaviors.

Contribution

It provides a numerical analysis of Lifshitz scaling effects on holographic p-wave superconductors with nonlinear electrodynamics, highlighting how critical temperature and conductivity are impacted.

Findings

Critical temperature decreases with increasing nonlinear parameter, Lifshitz exponent, or mass.

Real part of conductivity shows delta function behavior at low frequencies.

Large frequency behavior follows Re[σ]=ω^{D-4}.

Abstract

We employ gauge/gravity duality to study the effects of Lifshitz scaling on the holographic $p$ wave superconductors in the presence of Born-Infeld (BI) nonlinear electrodynamics. By using the shooting method in the probe limit, we calculate the relation between critical temperature $T_{c}$ and $\rho^{z/d}$ numerically for different values of mass, nonlinear parameter $b$ and Lifshitz critical exponent $z$ in various dimensions. We observe that critical temperature decreases by increasing $b$, $z$ or the mass parameter $m$ which makes conductor/superconductor phase transition harder to form. In addition, we analyze the electrical conductivity and find the behavior of real and imaginary parts as a function of frequency which depend on the model parameters. However, some universal behaviors are seen. For instance at low frequencies, real part of conductivity shows a delta function behavior while the imaginary part has a pole which means that these two parts are connected to each other through Kramers-Kronig relation. The behavior of real part of conductivity in the large frequency regime can be achieved by $Re[\sigma]=\omega^{D-4}$. Furthermore, with increasing the Lifshitz scaling $z$, the energy gap and the minimum values of the real and imaginary parts become unclear.