Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 156, Issue 3, Pages 417-426Publisher
SPRINGER
DOI: 10.1007/s10955-014-0992-0
Keywords
Graphene; Integer quantum Hall effect; Bulk-edge correspondence; Chern number
Categories
Funding
- ERC
- Swiss National Science Foundation
Ask authors/readers for more resources
We rely on a recent method for determining edge spectra and we use it to compute the Chern numbers for Hofstadter models on the honeycomb lattice having rational magnetic flux per unit cell. Based on the bulk-edge correspondence, the Chern number is given as the winding number of an eigenvector of a transfer matrix, as a function of the quasi-momentum . This method is computationally efficient (of order in the resolution of the desired image). It also shows that for the honeycomb lattice the solution for for flux in the -th gap conforms with the Diophantine equation , which determines . A window such as , or possibly shifted, provides a natural further condition for , which however turns out not to be met. Based on extensive numerical calculations, we conjecture that the solution conforms with the relaxed condition sigma(H) is an element of (-q, q).
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available