2008/12/15 by K. Ziegler, Klaus Ziegler, Balázs Dóra +1 · 1 citation
Materials Science · Physics and Astronomy · #Graphene research and applications #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.dis-nn #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.79.235431
published as Phys. Rev. B 79, 235431 (2009) · 12 pages, 10 figures
arxiv created 2008/12/15 · openalex publication_date 2009/06/24 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 behavior 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 on the HCL in the presence of random vector potential. A careful investigation of the lowest eigenvalues indeed indicates 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 behavior.