Electronic Structure in Gapped Graphene with Coulomb Potential

TL;DR

This paper numerically investigates bound and quasi-bound electron states in gapped graphene with Coulomb impurities, comparing lattice and continuum models, and proposes experiments to observe supercritical vacuum decay.

Contribution

It provides a detailed numerical analysis of impurity-induced states in gapped graphene and bridges lattice simulations with continuum Dirac models, including experimental proposals.

Findings

Numerical results match continuum predictions for bound states.

Identification of quasi-bound states in supercritical regime.

Design of experiments to observe supercritical vacuum decay.

Abstract

In this paper, we numerically study the bound electron states induced by long range Coulomb impurity in gapped graphene and the quasi-bound states in supercritical region based on the lattice model. We present a detailed comparison between our numerical simulations and the prediction of the continuum model which is described by the Dirac equation in (2+1)-dimensional Quantum Electrodynamics (QED). We also use the Fano's formalism to investigate the quasi-bound state development and design an accessible experiments to test the decay of the supercritical vacuum in the gapped graphene.