Effect of topological defects and Coulomb charge on the low energy quantum dynamics of gapped graphene

TL;DR

This paper investigates how topological defects and Coulomb impurities influence the quantum behavior of gapped graphene, revealing critical charge thresholds and boundary condition sensitivities relevant for experimental observations.

Contribution

It introduces a comprehensive analysis of the combined effects of topological defects and Coulomb charges on gapped graphene's quantum dynamics, including boundary condition classification and observable sensitivities.

Findings

Quantum instability occurs beyond a critical Coulomb charge.

Boundary conditions in gapped graphene cones depend on a single real parameter.

Observable quantities are sensitive to boundary condition parameters.

Abstract

We study the combined effect of a conical topological defect and a Coulomb charge impurity on the dynamics of Dirac fermions in gapped graphene. Beyond a certain strength of the Coulomb charge, quantum instability sets in, which demarcates the boundary between sub and supercritical values of the charge. In the subcritical regime, for certain values of the system parameters, the allowed boundary conditions in gapped graphene cone can be classified in terms of a single real parameter. We show that the observables such as local density of states, scattering phase shifts and the bound state spectra are sensitive to the value of this real parameter, which is interesting from an empirical point of view. For a supercritical Coulomb charge, we analyze the system with a regularized potential as well as with a zigzag boundary condition and find the effect of the sample topology on the observable features of the system.