Effective Lagrangian and Topological Interactions in Supersolids

TL;DR

This paper develops a low-energy effective Lagrangian for supersolids, revealing a topological coupling between superfluid and crystalline modes, with implications for defect interactions and phonon scattering.

Contribution

It introduces a novel topological term in the effective Lagrangian that captures superfluid-crystal interactions in supersolids, especially relevant for defect dynamics.

Findings

Topological coupling dominates defect-related phenomena in supersolids.

Derived a model-independent scattering cross section for phonons by vortices.

Constraints from Galilean invariance shape the effective Lagrangian form.

Abstract

We construct a low-energy effective Lagrangian describing zero-temperature supersolids. Galilean invariance imposes strict constraints on the form of the effective Lagrangian. We identify a topological term in the Lagrangian that couples superfluid and crystalline modes. For small superfluid fractions this interaction term is dominant in problems involving defects. As an illustration, we compute the differential cross section of scatterings of low-energy transverse elastic phonons by a superfluid vortex. The result is model-independent.