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

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.