Skyrmions in a Hole Gas with Large Spin Gap and Strong Disorder

Abstract

Skyrmion [1] is a topological spin excitation of a polarized ground state, energetically favored over a single spin flip due to the tendency for parallel alignment of neighboring spins (i.e., to minimize gradient of the spin projection density). Under certain conditions, it also occurs [2] as an elementary charge excitation in quantum Hall systems, that is in a two-dimensional (2D) system of charge carriers (electrons or holes) in a strong magnetic field B, yielding filling of at most a small number of the Landau levels (LLs). The LL occupation is conveniently defined by a filling factor ν = 2π%λ, where % is the sheet concentration and λ = √ hc/eB is the magnetic length. At the exact filling of the lowest spin-polarized LL, corresponding to ν = 1, the ground state is spin polarized even in the absence of the single-particle Zeeman spin splitting EZ = gμBB (g being the Lande factor). This situation can be described as half-filling of the lowest (n = 0) spin-degenerate LL. The reason is the dominant tendency to maximize exchange. The spin-polarized ν = 1 state is an example of quantum Hall ferromagnet. Remarkably, the spin polarization at EZ = 0 is sensitive to the LL filling. In ideal 2D (zero width) it occurs at any integral ν [3] and also at the Laughlin series of fractions ν = (2p + 1)−1 with integral p [4], but not at nearly any other fraction. It also strongly depends on