@article{oai:tsukuba.repo.nii.ac.jp:00014894,
 author = {初貝, 安弘 and Hatsugai, Y. and Fukui, T. and Aoki, H.},
 issue = {1},
 journal = {The European physical journal. ST, special topics},
 month = {Sep},
 note = {application/pdf, We discuss topological aspects of electronic properties of graphene, including
edge effects, with the tight-binding model on a honeycomb lattice and its
extensions to show the following: (i) Appearance of the pairn of massless Dirac
dispersions, which is the origin of anomalous properties including a peculiar quantum
Hall effect (QHE), is not accidental to honeycomb, but is rather generic for
a class of two-dimensional lattices that interpolate between square and !-flux lattices.
Persistence of the peculiar QHE is interpreted as a topological stability. (ii)
While we have the massless Dirac dispersion only around E = 0, the anomalous
QHE associated with the Dirac cone unexpectedly persists for a wide range of
the chemical potential. The range is bounded by van Hove singularities, at which
we predict a transition to the ordinary fermion behavior acompanied by huge
jumps in the QHE with a sign change. (iii) For edges we establish a coincidence
between the quantum Hall effect in the bulk and the quantum Hall effect for the
edge states, which is a manifestation of the topological bulk-edge correspondence.
We have also explicitly shown that the E = 0 edge states in honeycomb in zero
magnetic field persist in magnetic field.},
 pages = {133--141},
 title = {Topological aspects of graphene - Dirac fermions and the bulk-edge correspondence in magnetic fields},
 volume = {148},
 year = {2007}
}