Wave packet dynamical simulation of quasiparticle interferences in 2D materials

Materials consisting of single- or a few atomic layers have extraordinary physical properties, which are influenced by the structural defects. We present two calculation methods based on wave packet (WP) dynamics, where we compute the scattering of quasiparticle WPs on localized defects. The methods are tested on a graphene sheet: (1) We describe the perfect crystal lattice and the electronic structure by a local atomic pseudopotential, then calculate the Bloch eigenstates and build a localized WP from these states. The defect is represented by a local potential, then we compute the scattering by the time development of the WP. (2)We describe the perfect crystal entirely by the kinetic energy operator, then we calculate the scattering on the local defect described by the potential energy
operator. The kinetic energy operator is derived from the dispersion relation, which can be obtained from any electronic structure calculation. We also verify the method by calculating Fourier transform images and comparing them with experimental FFT-LDOS images from STM measurements. These calculation methods make it possible to study the quasiparticle interferences, inter- and intra-valley scattering, anisotropic scattering, etc., caused by defect sites for any 2D material.