Holographic Lifshitz superconductors: Analytic solution

TL;DR

This paper presents an analytic solution for Lifshitz holographic superconductors, enabling detailed analysis of their properties and establishing a dual Ginzburg-Landau theory with a fixed dynamic critical exponent.

Contribution

The authors derive an exact analytic solution for Lifshitz holographic superconductors and analyze their physical properties, including the critical exponent, which was previously unexplored.

Findings

Analytic solution for Lifshitz holographic superconductors

Identification of the dual Ginzburg-Landau theory with numerical coefficients

The dynamic critical exponent $z_d=2$ regardless of Lifshitz exponent $z$

Abstract

We construct an analytic solution for a one-parameter family of holographic superconductors in asymptotically Lifshitz spacetimes. We utilize this solution to explore various properties of the systems such as (1) the superfluid phase background and the grand canonical potential, (2) the order parameter response function or the susceptibility, (3) the London equation, (4) the background with a superfluid flow or a magnetic field. From these results, we identify the dual Ginzburg-Landau theory including numerical coefficients. Also, the dynamic critical exponent $z_d$ associated with the critical point is given by $z_d=2$ irrespective of the value of the Lifshitz exponent $z$.