Effective Field Theory for Acoustic and Pseudo-Acoustic Phonons in Solids

TL;DR

This paper develops a relativistic effective field theory describing interactions between acoustic and pseudo-acoustic phonons in solids, highlighting their Goldstone and pseudo-Goldstone nature, with applications to materials like bilayer graphene and dark matter detection.

Contribution

It introduces a novel effective field theory framework for acoustic and pseudo-acoustic phonons, incorporating small explicit symmetry breaking effects.

Findings

Derived the effective theory for 1D and 2D systems with isotropy.

Calculated the lifetime of phonons within this framework.

Applied the theory to real materials like bilayer graphene.

Abstract

We present a relativistic effective field theory for the interaction between acoustic and gapped phonons in the limit of a small gap. We show that, while the former are the Goldstone modes associated with the spontaneous breaking of spacetime symmetries, the latter are pseudo-Goldstones associated with some (small) explicit breaking. We hence dub them "pseudo-acoustic" phonons. In this first investigation, we build our effective theory for the cases of one and two spatial dimensions, two atomic species, and assuming large distance isotropy. As an illustrative example, we show how the theory can be applied to compute the total lifetime of both acoustic and pseudo-acoustic phonons. This construction can find applications that range from the physics of bilayer graphene to sub-GeV dark matter detectors.