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Topological aspects of graphene - Dirac fermions and the bulk-edge correspondence in magnetic fields
初貝, 安弘
Hatsugai, Y.
Fukui, T.
Aoki, H.
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.
journal article
Springer Berlin
2007-09
application/pdf
The European physical journal. ST, special topics
1
148
133
141
http://hdl.handle.net/2241/97689
1951-6355
AA12197316
https://tsukuba.repo.nii.ac.jp/record/14894/files/EPJ-ST_148-1.pdf
eng
10.1140/epjst/e2007-00233-5
© 2007 Springer