Hierarchy of spin and valley symmetry breaking in quantum Hall single-layer graphene

Several microscopic mechanisms for breaking the fourfold degeneracy of the central Landau level in a single-layer graphene is examined. We consider valley-scattering random potential, Zeeman interaction, and electron-phonon coupling as potential candidates to break the SU(4) symmetry of the Coulomb exchange interaction. A phase diagram is worked out, giving either the "spin-first" or "valley-first" splitting of the central Landau levels depending on the relative strengths of the electron-phonon coupling and the Zeeman interaction. Existence of a midgap band at the domain wall separating Landau levels of opposite valley polarity is demonstrated.