Dissipation induced elastic-mode instability with topological excitation in holographic non-equilibrium steady cnoidal wave supersolid

TL;DR

This paper investigates the stability of cnoidal wave supersolids at finite temperature using a holographic model, revealing elastic-mode instabilities linked to topological excitations and dissipation effects.

Contribution

It introduces a finite temperature holographic framework to analyze the dynamical stability of cnoidal wave supersolids, highlighting the role of elastic-mode instabilities and topological excitations.

Findings

Cnoidal wave supersolids are dynamically unstable at finite temperature.

Elastic Goldstone modes drive the instability and topological excitation nucleation.

Elastic-mode instability dominates wave collisions in high dissipation regimes.

Abstract

The possible existence of an exotic phase of matter rigid like a solid but able to sustain persistent and dissipation-less flow like a superfluid, a "supersolid", has been the subject of intense theoretical and experimental efforts since the discovery of superfluidity in Helium-4. Recently, it has been proposed that nonlinear periodic modulations known as cnoidal waves, that naturally emerge in Bose-Einstein condensates, provide a promising platform to find and study supersolidity in non-equilibrium phases of matter. Nevertheless, so far the analysis has been limited to a one-dimensional zero-temperature system. By combining the dissipative Gross-Pitaevskii equation with a finite temperature holographic model, we show that the proposed cnoidal wave supersolid phases of matter are dynamically unstable at finite temperature. We ascribe this instability to the dynamics of the "elastic" Goldstone mode, which arises as a direct consequence of translational order in the presence of dissipation, and establish a direct connection between the elastic-mode instability of the supersolid state and the nucleation of topological excitations during the relaxation towards a homogeneous equilibrium state, which resembles the Landau instability in superfluids. Finally, we numerically confirm the dominant role of the elastic-mode instability in the collision between cnoidal waves in the strong dissipation limit.