Regularization of the spectral problem for the monolayer graphene with the separable in the angular momentum representation singular potential of defect

TL;DR

This paper investigates the electronic states in monolayer graphene with a short-range, angular momentum-dependent defect potential, using a (2+1)-D Dirac equation approach to regularize the singular boundary problem.

Contribution

It introduces a momentum representation method to regularize the spectral problem for graphene with singular defect potentials, providing a new approach to analyze bound and resonance states.

Findings

Derived a characteristic equation for bound and resonance states

Compared new regularization method with previous approaches

Achieved satisfactory regularization of the boundary problem

Abstract

The electronic states in the monolayer graphene with the short-range perturbation asymmetric with respect to the band index are analized. The study was made for the separable in the angular momentum representation potential basing on the (2+1)-dimensional Dirac equation. The characteristic equation for bound and resonance states obtained in the present paper is compared with one derived earlier for the same problem with different approach. The momentum representation approach used in the present paper allowed us to obtain the satisfactory regularization of the Hadamar incorrect boundary problem stemming from the potential singularity.