“…In recent years, by using the low-energy Dirac Hamiltonian [ 4 ], we have extensively explored varieties of dynamical properties of electrons in graphene and other two-dimensional materials, including Landau quantization [ 18 , 31 , 32 , 33 , 34 , 35 ], many-body optical effects [ 36 , 37 , 38 , 39 , 40 , 41 ], band and tunneling transports [ 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 ], etc. In this paper, we particularly focus on the application of computed electronic states and band structures from a tight-binding model to the calculations of Coulomb and impurity scatterings of electrons in graphene on the basis of a many-body theory [ 3 , 4 ], where the former and latter determine the lineshape [ 1 ] of an absorption peak and the transport mobility [ 44 ], respectively.…”