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

We study generalized spin waves in graphene under a strong magnetic field when the Landau-level filling factor is nu = +/- 1. In this case, the ground state is a particular SU(4) quantum Hall ferromagnet, in which not only the physical spin is fully polarized but also the pseudospin associated with the valley degree of freedom. The nature of the ground state and the spin-valley polarization depend on explicit symmetry-breaking terms that are also reflected in the generalized spin-wave spectrum. In addition to pure spin waves, one encounters valley-pseudospin waves as well as more exotic entanglement waves that have a mixed spin-valley character. Most saliently, the SU(4) symmetry-breaking terms not only yield gaps in the spectra, but also under certain circumstances, namely, in the case of residual ground-state symmetries, render the originally quadratic (in the wave vector) spin-wave dispersion linear.