Quantum Hall Skyrmion Lattices at $g \approx 0$

TL;DR

This paper studies the classical ground states of large, overlapping skyrmions in quantum Hall systems at zero g-factor, revealing a rectangular lattice with Ne9el order and zero spin polarization, with implications for experiments.

Contribution

It demonstrates that at zero g-factor, skyrmions form a rectangular lattice with Ne9el order and zero spin polarization, extending understanding of skyrmion arrangements in quantum Hall systems.

Findings

Ground state is a rectangular skyrmion lattice with Ne9el order.

Charge distribution exhibits face-centered rectangular symmetry.

Spin polarization vanishes at g=0 under various conditions.

Abstract

We investigate the classical ground state configurations of a collection of skyrmions in the limit of vanishing L\'ande $g$ factor. We show that in this limit, the skyrmions which are large and overlapping, behave qualitatively differently from small skyrmions. We investigate the system in various regimes of spin stiffness. We find that in all regimes, at $g=0$, the ground state configuration is a rectangular skyrmion lattice with N\'eel orientational ordering. The charge distribution has a higher symmetry of a face-centered rectangular lattice and the $z$-component of the spin polarization is zero. We also present general argument for the vanishing of spin polarization at $g=0$ at finite temperature and in the presence of disorder and discuss some experimental consequences of our results.