The field theory of Skyrme lattices in quantum Hall ferromagnets

TL;DR

This paper models multi-skyrmion configurations in quantum Hall ferromagnets using nonlinear sigma models, revealing phase transitions between different lattice structures and potential topological deformations at low Zeeman energies.

Contribution

It introduces a Skyrme lattice framework for quantum Hall ferromagnets, analyzing phase transitions and skyrmion interactions with quantum fluctuations.

Findings

Ground state is a ferromagnet triangular Skyrme lattice near ν=1.

Transition to an antiferromagnet square lattice with increasing skyrmion density.

Skyrmion with charge two can be energetically favorable at low Zeeman energy.

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 $g \leq g_c$. 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.