SU(N)quantum Hall skyrmions

Abstract

We have investigated skyrmions in N-component quantum Hall (QH) systems. We find that $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ skyrmions are the lowest-energy charged excitations for filling factors $\nu =1,2,\dots ,N-1$ for small enough symmetry breaking terms. $N>\mathrm{}2\mathrm{}$ skyrmions can be realized in Si QH systems based on the (110) or (111) interfaces of Si, or perhaps in Si (100) systems, where the spin and valley isospin together provide an SU(4)-symmetry, or in multilayer QH systems. We also present Hartree-Fock results for a phenomenological easy-axis SU(2)-breaking model appropriate to valley degeneracy.