Skyrme Crystal in a Two-Dimensional Electron Gas

The ground state of a two-dimensional electron gas at Landau level filling factors near $\nu =1\mathrm{}$ is a Skyrme crystal with long-range order in the positions and orientations of the topologically and electrically charged elementary excitations of the $\nu =1\mathrm{}$ 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.