Structural Transitions of a Soft Solid: The Skyrmion Lattice

Abstract

Skyrmions, also called charged spin texture exitations (CSTE) are quasiparticles in Quantum Hall systems with spin, near the filling factor v = 1. At this filling factor the ground state is ferromagnetic. When one electron is added or removed from the system, the resulting quasiparticle is an extended object, with total spin significantly greater than 1/2. When v deviates from 1, there is a finite density of skyrmions present which, at zero temperature, are expected to crystallize. We show within the context of a nonlinear sigma model, that the classical ground state away from v = 1 is a skyrmion crystal with a generalised Néel order. We show that as a function of the filling v, the skyrmion crystal undergoes a triangle → square transition at zero temperature. This novel structural transition should persist at nonzero temperature and may be probed experimentally.