We propose a -symmetrically deformed version of the graphene tight-binding model under a magnetic field. We analyse the structure of the spectra and the eigenvectors of the Hamiltonians around the K and K′ points, both in the -symmetric and -broken regions. In particular, we show that the presence of the deformation parameter V produces several interesting consequences, including the asymmetry of the zero-energy states of the Hamiltonians and the breakdown of the completeness of the eigenvector sets. We also discuss the biorthogonality of the eigenvectors, which turns out to be different in the -symmetric and -broken regions.
- Received May 18, 2016.
- Accepted August 25, 2016.
- © 2016 The Author(s)
Published by the Royal Society. All rights reserved.