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.

💡 Research Summary

This paper presents a comprehensive theoretical framework for incorporating electrostatic screening into the tight‑binding description of graphene, using an extended Binding‑Energy and Bond‑Charge (BBC) model. The authors first identify the shortcomings of conventional tight‑binding approaches, which typically consider only nearest‑neighbor hopping and employ the bare Coulomb potential, leading to singularities at short distances and neglect of long‑range screening. To overcome these issues, they introduce a screened BBC potential of the form

 V_BBC(R) = (Z – σ_core – σ_v) e²/(4πϵ₀ R) exp(‑R/λ),

where σ_v is a tunable screening parameter that reflects the surrounding charge environment. σ_v is not a fixed constant; instead, it is made adaptive through a machine‑learning (ML) model that maps local chemical descriptors D_A onto σ_v, yielding an ML‑BBC potential.

Within this framework, the on‑site energy ε_i is expressed as ε₀ + β σ_v + γ V_BBC(R), and the hopping integrals acquire an exponential decay and a bounded tanh modulation:

 t_ij(R) = t₀ exp(‑R/λ_t) tanh