Hydrodynamic theory of supersolids: Variational principle and effective Lagrangian

TL;DR

This paper develops a comprehensive low-energy theory for supersolids, capturing the coupling between superfluidity and solid elasticity, and predicts observable second sound modes in response functions.

Contribution

It introduces a variational principle-based effective Lagrangian for supersolids, integrating symmetry and conservation laws to describe their collective excitations.

Findings

Peaks in response functions indicate second sound modes.

The theory links supersolidity with existing superfluid and solid models.

Conservation laws determine the number and nature of collective modes.

Abstract

We develop an effective low-energy, long-wavelength theory of a bulk supersolid--a putative phase of matter with simultaneous crystallinity and Bose condensation. Using conservation laws and general symmetry arguments we derive an effective action that correctly describes the coupling between the Bose condensation and the elasticity of the solid. We use our effective action to calculate the correlation and response functions for the supersolid, and we show that the onset of supersolidity produces peaks in the response function, corresponding to propagating second sound modes in the solid. Throughout our work we make connections to existing work on effective theories of superfluids and normal solids, and we underscore the importance of conservation laws and symmetries in determining the number and character of the collective modes.