Characteristic edge states of quantum Hall effects in graphene: Dirac fermions and quantum liquids

Yasuhiro Hatsugai

University of Tsukuba, Japan

Gapped quantum liquids are featureless in the sense that there is no characteristic low energy quasiparticles and also absence of the spontaneous symmetry breaking. However, with geometrical (topological) perturbation such as existence of boundaries or impurities, localized degrees of freedom inevitably appear as generic edge states, which themselves characterize the quantum liquids. Typical examples are quantum Hall edge (QH) states and S=1/2 effective boundary spins in the integer spin chains. In graphene as the condensed matter realization of Dirac fermion, the edge states in the QH effects are also special reflecting its honeycomb lattice structure. After general discussion of the edge states in the quantum liquids, characteristic edge states of the graphene QHE are described from a topological point of view. Effects of interaction will be also discussed.