Theory of real supersolids

TL;DR

This paper reviews the properties of supersolids, discusses their theoretical description based on symmetries, and proposes a mean-field model using the Gross-Pitaevskii equation to understand their dynamics.

Contribution

It provides a comprehensive theoretical framework for supersolids, combining symmetry-based equations and a mean-field model to explore their properties and existence conditions.

Findings

Supersolids can exhibit both elastic behavior and superfluidity.

Supersolid states are expected at very low temperatures with small superfluid fractions.

A mean-field model based on the Gross-Pitaevskii equation captures key supersolid properties.

Abstract

We review the main properties of a supersolid. We describe first the macroscopic equation that satisfies a supersolid based on general arguments and symmetries and show that such solids might exhibit simultaneously or independently both elastic behavior and superfluidity. We then explain why a supersolid state should exist for solids at very low temperature but with a very small superfluid fraction. Finally, we propose a mean-field model, based on the Gross-Pitaevski\u{\i} equation, which presents the general properties expected for a supersolid and should therefore provide a consistent framework to study its dynamical properties.