The field theory of Skyrme lattices in quantum Hall ferromagnets

Details The field theory of Skyrme lattices in quantum Hall ferromagnets The field theory of Skyrme lattices in quantum Hall ferromagnets

1997-05-22

arxiv.org/abs/cond-mat/9705224v1

Phys.Rev. B58 (1998) 10665

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

17 pages

Scientific paper

10.1103/PhysRevB.58.10665

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 $g \leq g_c$. 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.

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