SU(4) spin waves in the ν=±1 quantum Hall ferromagnet in graphene

Abstract

The lowest energy excitations of a quantum Hall ferromagnet are generalized SU(4) spin waves that can be real spin, valley pseudospin waves, or mixed spin-valley waves (see image). In this paper, the dispersion relations of these different SU(4) spin-wave types are investigated based on the phase diagram of the quantum Hall ferromagnet at filling factor $\ensuremath{\nu}=\ifmmode\pm\else\textpm\fi{}1$. In three of the four phases, there can be one or more linearly dispersing modes at low energy, due to a remaining symmetry in the residual anisotropies.