Shape-deformation-driven structural transitions in quantum hall skyrmions

Abstract

The quantum Hall ground state away from ν = 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 ν = 1 is a Skyrmion crystal with a generalized Néel order. As a function of filling factor ν and Landé factor g, the Skyrmion crystal undergoes a triangle --> square --> triangle transition at zero temperature. We argue that this structural transition is driven by a change in the shape of the individual Skyrmions and may be probed experimentally. Quantum fluctuations lead to an orientationally disordered phase at low Skyrmion densities.