Comment on "Impurity spectra of graphene under electric and magnetic fields"

TL;DR

This paper critiques a previous study on impurity spectra in graphene under electric and magnetic fields, clarifying the limitations of earlier results and providing corrected numerical spectra for all impurity charge strengths.

Contribution

It offers a corrected numerical analysis of Coulomb impurity spectra in graphene, addressing previous inaccuracies and extending results to higher impurity charges with proper regularization.

Findings

Previous results limited to charge |α| ≤ 0.5 are insufficient for higher charges.

Proper regularization is necessary for accurate spectra at |α| > 0.5.

Corrected spectra are provided for arbitrary impurity charges.

Abstract

In a recent publication [Phys. Rev. B $\textbf{89}$, 155403 (2014)], the authors investigated the spectrum of a Coulomb impurity in graphene in the presence of magnetic and electric fields using the coupled series expansion approach. In the first part of their publication they investigated how Coulomb impurity states collapse in the presence of a perpendicular magnetic field. We argue that the obtained spectrum does not give information about the atomic collapse and that their interpretation of the spectrum regarding atomic collapse is not correct. We also argue that the obtained results are only valid up to the dimensionless charge $\mid \alpha\mid=0.5$ and in order to obtain correct results for $\alpha>0.5$ a proper regularisation of the Coulomb interaction is required. Here we present the correct numerical results for the spectrum for arbitrary values of $\alpha$.