Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-like low-energy excitations. When Zeeman and spin-orbit interactions are neglected, its Landau levels are fourfold degenerate, explaining the 4e2/h separation between quantized Hall conductivity values seen in recent experiments. In this Letter we derive a criterion for the occurrence of interaction-driven quantum Hall effects near intermediate integer values of e2/h due to charge gaps in broken symmetry states.

Motivated by recent graphene transport experiments, we undertake a numerical study of the conductivity of disordered two-dimensional massless Dirac fermions. Our results reveal distinct differences between the cases of short-range and Coulomb randomly distributed scatterers. We speculate that this behavior is related to the Boltzmann transport theory prediction of dirty-limit behavior for Coulomb scatterers.

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We report successful spin injection into the surface states of topological insulators by using a spin pumping technique. By measuring the voltage that shows up across the samples as a result of spin pumping, we demonstrate that a spin-electricity conversion effect takes place in the surface states of bulk-insulating topological insulators Bi(1.5)Sb(0.5)Te(1.7)Se(1.3) and Sn-doped Bi(2)Te(2)Se. In this process, the injected spins are converted into a charge current along the Hall direction due to the spin-momentum locking on the surface state.