Excitations of a two-dimensional supersolid

TL;DR

This paper provides a theoretical analysis of the excitation spectrum in two-dimensional supersolid Bose-Einstein condensates with dipole-dipole or soft-core interactions, revealing three gapless modes and their relation to broken symmetries.

Contribution

It introduces a detailed numerical and hydrodynamic analysis of excitations in 2D supersolids, highlighting differences between dipolar and soft-core interaction cases.

Findings

Three gapless excitation branches identified

Sound speeds described by hydrodynamic theory with elastic parameters

Distinct excitation characteristics for dipolar and soft-core supersolids

Abstract

We present a theoretical study of the excitations of the two-dimensional supersolid state of a Bose-Einstein condensate with either dipole-dipole interactions or soft-core interactions. This supersolid state has three gapless excitation branches arising from the spontaneously broken continuous symmetries. Two of these branches are related to longitudinal sound waves, similar to those in one-dimensional supersolids. The third branch is a transverse wave arising from the non-zero shear modulus of the two-dimensional crystal. We present the results of numerical calculations for the excitations and dynamic structure factor characterising the density fluctuations, and study their behavior across the discontinuous superfluid to supersolid transition. We show that the speeds of sound are described by a hydrodynamic theory that incorporates generalized elastic parameters, including the shear modulus. Furthermore, we establish that dipolar and soft-core supersolids manifest distinct characteristics, falling into the bulk incompressible and rigid lattice limits, respectively.