Skymrion lattice melting in the quantum Hall system

TL;DR

This paper investigates the melting and disordering of skyrmion lattices in quantum Hall systems using a combined RG and Coulomb gas approach, revealing complex phase transitions and a rich zero-temperature phase diagram.

Contribution

It introduces a novel theoretical framework combining RG and Coulomb gas methods to analyze skyrmion lattice melting in quantum Hall systems, including a classical model and phase diagram.

Findings

Multiple melting/disordering scenarios for different lattice types.

Identification of a centered rectangular phase separating triangular and square lattices.

Rich T=0 phase diagram with various stable phases.

Abstract

The melting and magnetic disordering of the skyrmion lattice in the quantum Hall system at filling factor $\nu\approx 1$ are studied. A Berezinskii-Kosterlitz-Thouless renormalization group theory is employed to describe the coupled magnetic and translational degrees of freedom. The non-trivial magnetic properties of the skyrmion system stem from the in-plane components of the non-collinear magnetization in the vicinity of skyrmions, which are described by an antiferromagnetic XY model. In a Coulomb gas formulation the `particles' are the topological defects of the XY model (vortices) and of the lattice (dislocations and disclinations). The latter frustrate the antiferromagnetic order and acquire fractional vorticity in order to minimize their energy. We find a number of melting/disordering scenarios for various lattice types. While these results do not depend on a particular model, we also consider a simple classical model for the skyrmion system. It results in a rich T=0 phase diagram. We propose that the triangular and square skyrmion lattices are generically separated by a centered rectangular phase in the quantum Hall system.