Skyrmions in Higher Landau Levels

TL;DR

This paper calculates the energies of skyrmions in higher Landau levels and finds they are not the lowest energy excitations except at certain filling factors, contrasting with the known behavior at filling factor 1.

Contribution

It provides a detailed energy analysis of skyrmions at odd integer filling factors greater than 1, showing they are not energetically favorable as quasiparticles in these cases.

Findings

Skyrmions have higher energy than fully polarized quasiparticles at filling factors 2k+1 for k ≥ 1.

Skyrmions are only relevant quasiparticles at filling factors 1, 1/3, and 1/5.

The energy hierarchy of quasiparticles differs from the case at filling factor 1.

Abstract

We calculate the energies of quasiparticles with large numbers of reversed spins (``skyrmions'') for odd integer filling factors 2k+1, k is greater than or equals 1. We find, in contrast with the known result for filling factor equals 1 (k = 0), that these quasiparticles always have higher energy than the fully polarized ones and hence are not the low energy charged excitations, even at small Zeeman energies. It follows that skyrmions are the relevant quasiparticles only at filling factors 1, 1/3 and 1/5.