The field theory of Skyrme lattices in quantum Hall ferromagnets

Abstract

We report the application of the nonlinear $\sigma$ model to study the multi-skyrmion problem in the quantum Hall ferromagnet system. We show that the ground state of the system can be described by a ferromagnet triangular Skyrme lattice near $\nu =1$ where skyrmions are extremely dilute. We find a transition into antiferromagnet square lattice by increasing the skyrmion density and therefore $|\nu -1|$. We investigate the possibility that the square Skyrme lattice deforms to a single skyrmion with the same topological charge when the Zeeman energy is extremely smaller than the Coulomb energy. We explicitly show that the energy of a skyrmion with charge two is less than the energy of two skyrmions each with charge one when $g\le g_c$. By taking the quantum fluctuations into account, we also argue the possibility of the existence of a non-zero temperature Kosterlitz-Thouless and a superconductor-insulator phase transition.

17 pages

References in corpus (5)

• Collective Excitations, NMR, and Phase Transitions in Skyrme Crystals
• A critical comparison of classical field theory and microscopic wavefunctions for skyrmions in quantum Hall ferromagnets
• Quantum Hall Skyrmions with Higher Topological Charge
• Shape Deformation driven Structural Transitions in Quantum Hall Skyrmions
• Quantum fluctuations of classical skyrmions in quantum Hall Ferromagnets

Cited by in corpus (2)

• Pinning mode resonance of a Skyrme crystal near Landau level filling factor $\nu$=1
• Towards a phase diagram of the 2D Skyrme model