Local density of states in disordered graphene

Details Local density of states in disordered graphene Local density of states in disordered graphene

2008-12-15

arxiv.org/abs/0812.2790v1

Phys. Rev. B 79, 235431 (2009)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

12 pages, 10 figures

Scientific paper

10.1103/PhysRevB.79.235431

We study two lattice models, the honeycomb lattice (HCL) and a special square lattice (SQL), both reducing to the Dirac equation in the continuum limit. In the presence of disorder (gaussian potential disorder and random vector potential), we investigate the behaviour of the density of states (DOS) numerically and analytically. While an upper bound can be derived for the DOS on the SQL at the Dirac point, which is also confirmed by numerical calculations, no such upper limit exists for the HCL in the presence of random vector potential. A careful investigation of the lowest eigenvalues indeed indicate, that the DOS can possibly be divergent at the Dirac point on the HCL. In spite of sharing a common continuum limit, these lattice models exhibit different behaviour.

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