Topological Aspects of Fermions on a Honeycomb Lattice

D Chakrabarti, S Hands, A Rago

Research output: Contribution to journalArticlepeer-review

Abstract

We formulate a model of relativistic fermions moving in two Euclidean dimensions based on a tight-binding model of graphene. The eigenvalue spectrum of the resulting Dirac operator is solved numerically in smooth U(1) gauge field backgrounds carrying an integer-valued topological charge Q, and it is demonstrated that the resulting number of zero-eigenvalue modes is in accord with the Atiyah-Singer index theorem applied to two continuum flavors. A bilinear but gauge non-invariant chirality operator appropriate for distinguishing the topological zero modes is identified. When this operator is used to calculate Q, it is found that the maximum topological charge capable of being measured in this fashion scales with the perimeter of the lattice. Some concluding remarks compare these results to what is known for staggered lattice fermions.
Original languageEnglish
Number of pages0
JournalJHEP
Volume906
Issue number0
Publication statusPublished - 8 Apr 2009

Keywords

  • hep-lat

Fingerprint

Dive into the research topics of 'Topological Aspects of Fermions on a Honeycomb Lattice'. Together they form a unique fingerprint.

Cite this