Topological aspects of graphene: Dirac fermions and the bulk-edge correspondence in magnetic fields

Details Topological aspects of graphene: Dirac fermions and the bulk-edge correspondence in magnetic fields Topological aspects of graphene: Dirac fermions and the bulk-edge correspondence in magnetic fields

2007-01-18

arxiv.org/abs/cond-mat/0701431v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

8 pages, 5 figures, proceeding of the graphene conference at MPIPKS Dresden, Sep. 25-Oct.1, 2006

Scientific paper

10.1140/epjst/e2007-00233-5

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 $\pi$-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.

Affiliated with

Also associated with

No associations

Rating

Topological aspects of graphene: Dirac fermions and the bulk-edge correspondence in magnetic fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Topological aspects of graphene: Dirac fermions and the bulk-edge correspondence in magnetic fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Topological aspects of graphene: Dirac fermions and the bulk-edge correspondence in magnetic fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-260930