Topological Defects Formation with Momentum Dissipation

TL;DR

This paper uses holographic methods to study how momentum dissipation affects topological defect formation in a strongly coupled superconductor during a temperature quench, finding minimal impact on scaling laws but increased defect density.

Contribution

It introduces a holographic model with graviton mass to analyze the influence of momentum dissipation on defect formation and proposes an analytic relation between coherence length and graviton mass.

Findings

Momentum dissipation has little effect on defect scaling laws.

Coherence length decreases with graviton mass.

Increased graviton mass leads to more topological defects.

Abstract

We employ holographic techniques to explore the effects of momentum dissipation on the formation of topological defects during the critical dynamics of a strongly coupled superconductor after a linear quench of temperature. The gravity dual is the dRGT massive gravity in which the conservation of momentum in the boundary field theory is broken by the presence of a bulk graviton mass. From the scaling relations of defects number and "freeze-out" time to the quench rate for various graviton masses, we demonstrate that the momentum dissipation induced by graviton mass has little effect on the scaling laws compared to the Kibble-Zurek mechanism. Inspired from Pippard's formula in condensed matter, we propose an analytic relation between the coherence length and the graviton mass, which agrees well with the numerical results from the quasi-normal modes analysis. As a result, the coherence length decreases with respect to the graviton mass, which indicates that the momentum dissipation will augment the number of topological defects.