Particles in non-Abelian gauge potentials - Landau problem and insertion of non-Abelian flux

Benoit Estienne, Shanna Haaker, Kareljan Schoutens

Published 2011-02-01, updated 2011-03-23Version 3

We study charged spin-1/2 particles in two dimensions, subject to a perpendicular non-Abelian magnetic field. Specializing to a choice of vector potential that is spatially constant but non-Abelian, we investigate the Landau level spectrum in planar and spherical geometry, paying particular attention to the role of the total angular momentum J = L +S. After this we show that the adiabatic insertion of non-Abelian flux in a spin-polarized quantum Hall state leads to the formation of charged spin-textures, which in the simplest cases can be identified with quantum Hall Skyrmions.