Holographic superconductors with $z=2$ Lifshitz scaling

TL;DR

This paper investigates holographic superconductors with Lifshitz scaling ($z=2$) using gauge/gravity duality, revealing unique low-temperature and high-frequency behaviors due to anisotropic black hole geometries.

Contribution

It introduces a numerical study of $z=2$ Lifshitz holographic superconductors, highlighting differences from AdS models in condensate and conductivity behaviors.

Findings

Condensate does not approach a constant at low temperature.

Conductivity approaches one from below at high frequency.

No peak in the imaginary part of AC conductivity for p-wave case.

Abstract

We use gauge/gravity duality to explore strongly coupled superconductors with dynamical exponent $z=2$. In the probe limit we numerically establish background solutions for the matter fields and plot the condensate versus the dimensionless temperature. We then investigate electromagnetic perturbations in order to compute the AC conductivity and also calculate the spectral function. Our results for the condensate and conductivity are qualitatively similar to those of the AdS superconductor. However, we find that (for both s- and p-wave) the condensate does not approach a constant at very low temperature and the conductivity goes to one from below but never exceeds it in the high frequency limit, in contrast to the AdS black hole. We do not see a peak at nonzero frequency in the imaginary part of the AC conductivity along the $x$ direction for the p-wave case. These features are due to the nontrivial dynamical exponent. To be specific, the black hole geometry considered in this work is anisotropic between space and time, very different from the Schwarzschild-AdS black hole, which results in different asymptotic behaviors of temporal and spatial components of gauge fields than those in the Schwarzschild-AdS black hole.