Hierarchy of Spin and Valley Symmetry Breaking in Quantum Hall Single Layer Graphene

الأصل · EN

We explore several microscopic mechanisms for breaking the n=0 fourfold Landau level degeneracy in a single-layer graphene. Valley-scattering random potential, Zeeman interaction, and electron-phonon coupling are considered in the presence of SU(4)-symmetric Coulomb exchange interaction. Among all the mechanisms considered, it is the electron-phonon coupling combined with the Zeeman interaction which leads to the full splitting of the n=0 Landau levels. A recent controversy of "valley-first" or "spin-first" breaking of SU(4) symmetry of the n=0 graphene Landau level is examined in light of our results. Existence of midgap states between Landau levels of opposite valley polarity are demonstrated.