Skyrme Crystal In A Two-Dimensional Electron Gas

TL;DR

This paper predicts that near filling factor , a two-dimensional electron gas forms a Skyrme crystal with specific lattice structure and spin-polarization properties, aligning well with experimental observations.

Contribution

It introduces the concept of a Skyrme crystal as the ground state near  and details its lattice structure and spin-polarization behavior, providing theoretical insight into experimental results.

Findings

Skyrme crystal forms a square lattice with opposing postures.

Calculated spin-polarization matches recent experimental data.

Ground state exhibits long-range order in excitations.

Abstract

The ground state of a two-dimensional electron gas at Landau level filling factors near $\nu =1$ is a Skyrme crystal with long range order in the positions and orientations of the topologically and electrically charged elementary excitations of the $\nu=1$ ferromagnetic ground state. The lowest energy Skyrme crystal is a square lattice with opposing postures for topological excitations on opposite sublattices. The filling factor dependence of the electron spin-polarization, calculated for the square lattice Skyrme crystal, is in excellent agreement with recent experiments.