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The field theory of Skyrme lattices in quantum Hall ferromagnets

M. Abolfath·M. R. Ejtehadi
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Abstract

We report the application of the nonlinear $σ$ 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 $ν=1$ where skyrmions are extremely dilute. We find a transition into antiferromagnet square lattice by increasing the skyrmion density and therefore $|ν-1|$. 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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M. Abolfath, M. R. Ejtehadi. 1997-05-22. The field theory of Skyrme lattices in quantum Hall ferromagnets. https://doi.org/10.1103/physrevb.58.10665

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