Trotter-Suzuki-time propagation method for calculating the density of states of disordered graphene

We present Trotter-Suzuki-time propagation method to calculate the Density of States (DOS) of disordered (i.e., vacancy and hydrogen adatom impurities) graphene system for the size of up to 16,000,000 atoms. The method is based on the numerical solution of Time-Dependent Schrodinger Equation (TDSE). Our calculation is focused on the case whereby the vacancy and hydrogen adatom impurities are mixed into one disordered system systematically. For a considerable high concentration of disorder, at low energy close to Fermi level, we found the band gap opening as the vacancy concentration is reduced, while the localized state remain stay at the Fermi level, which is in accordance with the previous calculation. In addition, the additional peaks occur at E/t=-2.972,-2.704,-2.435,-2.033,-0.959, and E/t=0.978,1.975,2.416,2.684,2.991, which are related to isolated carbon group. As for low concentration of disorder, the result gives a consistent picture of band gap opening and the occurrence of localized state. © 2018 Elsevier B.V.