Electrostatic Screening Modulation of Graphene's Electronic Structure and the Helical Wavefunction Dominated Topological Properties

This study examines electrostatic screening effects in graphene using tight binding calculations based on the Binding energy and Bond Charge model and a modified version of it. The results indicate that the modified BBC potential decays in an exponential manner with distance, which suppresses electron electron interactions. The hopping integrals exhibit a pronounced decrease over distance and shift with parameter variation. A band gap opens once the parameter exceeds a certain threshold. The density of states shows a prominent peak near the Fermi level, whereas the low-energy region remains largely unchanged. The low energy helical wave functions in graphene display topological characteristics, including pseudospin momentum locking and a π Berry phase, resulting in distinctive transport properties. By avoiding the Coulomb singularity, the model offers valuable insights for the engineering of screening in two-dimensional systems and the design of topological devices.