Singularity of density of states induced by random bond disorder in graphene

We re-investigate the effect of random bond disorder on the density of states (DOS) in graphene. Our large-scale calculation supports that there exists a critical disorder value gbc dividing the DOS into two distinct structures. In the regime gb0α>0): ρ(E)∼ρ1|E|αρ(E)∼ρ1|E|α (E   is Fermi energy with respect to the Dirac point, ρ1ρ1 is a constant). In the regime gb>gbc, it is observed that DOS develops a peak structure at the Dirac point E=0E=0. Through the finite-size scaling analysis, we elucidate that the DOS at the Dirac point diverges in the thermodynamics limit. Furthermore, it is found that the divergent behavior of DOS is sensitive to any on-site disorder which violates the chiral symmetry in graphene.