Shape Deformation driven Structural Transitions in Quantum Hall Skyrmions

TL;DR

This paper investigates how the shape deformation of skyrmions in quantum Hall systems leads to structural phase transitions in skyrmion crystals, revealing a triangle-square-triangle transition sequence driven by filling factor changes.

Contribution

It introduces a nonlinear sigma model analysis showing shape-driven structural transitions in skyrmion crystals, a novel insight into quantum Hall skyrmion behavior.

Findings

Skyrmion crystals exhibit a triangle to square to triangle transition as a function of filling factor.

The transition is driven by shape deformation of individual skyrmions.

The structural transition remains stable under thermal and quantum fluctuations.

Abstract

The Quantum Hall ground state away from $\nu = 1$ can be described by a collection of interacting skyrmions. We show within the context of a nonlinear sigma model, that the classical ground state away from $\nu = 1$ is a skyrmion crystal with a generalized N\'eel order. We show that as a function of filling $\nu$, the skyrmion crystal undergoes a triangle to square to triangle transition at zero temperature. We argue that this structural transition, driven by a change in the shape of the individual skyrmions, is stable to thermal and quantum fluctuations and may be probed experimentally.