Topological Phonon Modes in A Two-Dimensional Wigner Crystal

TL;DR

This paper explores how strong spin-orbit coupling can induce topological phonon modes in a 2D Wigner crystal, revealing chiral edge modes and discussing potential realizations in semiconductor structures.

Contribution

It demonstrates the theoretical possibility of topological phonon phases in Wigner crystals driven by spin-orbit coupling and analyzes their robustness and experimental prospects.

Findings

Chiral phonon edge modes exist in the topological phase.

Strong spin-orbit coupling can induce topological phonon states.

Weak spin-orbit coupling in typical systems is insufficient for topological transition.

Abstract

We investigate the spin-orbit coupling effect in a two-dimensional Wigner crystal. We show that sufficiently strong spin-orbit coupling and an appropriate sign of g-factor could transform the Wigner crystal to a topological phonon system. We demonstrate the existence of chiral phonon edge modes in finite size samples, as well as the robustness of the modes in the topological phase. We explore the possibility of realizing the topological phonon system in two-dimensional Wigner crystals confined in semiconductor quantum wells/heterostructure. We find that the spin-orbit coupling is too weak for driving a topological phase transition in these systems. We argue that one may look for the topological phonon system in correlated Wigner crystals with emergent effective spin-orbit coupling.