Shape-Deformation-Driven Structural Transitions in Quantum Hall Skyrmions

The quantum Hall ground state away from ν0ex0ex=0ex0ex1 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 ν0ex0ex=0ex0ex1 is a Skyrmion crystal with a generalized N\'eel order. As a function of filling factor ν and Land\'e 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.