Using Wavefront Dislocations to Probe Topological Berry Phase in Graphene With Multiple Scattering Centers

Defects in two dimensional materials offer a playground for interesting physics. Quasiparticle interference due to scattering caused by a single point defect in graphene leads to a visible interference pattern detectable in Scanning Tunneling Microscopy (STM) topography imaging. Points of singular phase known as dislocations appear visible in real space topography when filtering for momentum values associated with quasiparticle intervalley scattering. The integer number of dislocations corresponds to the topological Berry Phase of graphene. We investigate the interference pattern caused by two point defects in graphene at varying distances and track the behavior of the dislocations and the interaction between them as the defects get closer together. We use the python package PyBinding to calculate the spatial local density of states of a graphene lattice with two missing lattice points. Our work characterizes a length scale for when interference between the two scattering centers becomes relevant. Furthermore we use the results of the simulation to characterize an irregular defect in experimental data. We propose that this investigation can be used to improve characterization techniques of irregular defects in two dimensional materials, and develop a deeper understanding of the physics behind dislocations caused by two scattering centers.