Materials consisting of a single layer of atoms, often called two dimensional (2D) materials have many promising applications, due to their extraordinary physical properties. These properties, however, depend on the presence, density, and kind of structural defects present in the perfect 2D crystalline lattice. Electrons with energies falling into the allowed band, described by Bloch waves in quantum mechanics, propagate freely in a perfect crystal, but defects act as scattering centers for the Bloch waves. We studied the influence of different structural defects on the transport properties of a graphene lattice by calculating the scattering of electronic wave packets. We applied and compared two different methods. Within the first method, we describe the atomic lattice and the electronic structure of graphene by an atomic pseudopotential, then calculate the Bloch functions and corresponding E(kBloch) energies, where kBloch is the Bloch wave vector. The defect is represented by a local potential, then we compute the scattering by the time development of a wave packet composed of the Bloch waves. In the second method, however, we don’t need to calculate the wave functions, thus we also don’t need the graphene potential, because we incorporate the E(k) dispersion relation directly into the kinetic energy operator and the defect is still represented by a local potential. The dispersion relation can be a simple tight-binding (TB) dispersion relation, but for a more accurate representation of the electronic structure, we can utilize E(k) relations from an ab-initio DFT calculation.
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