Shape Deformation driven Structural Transitions in Quantum Hall Skyrmions

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.