In a recent paper [Phys. Rev. B 99, 155124 (2019)], the spectrum of a regularized Coulomb charge was studied in gapped pseudospin-1 systems generated by an $\alpha -{\mathcal{T}}_3$ lattice. The electronic spectrum was studied as a function of the impurity strength $Z\alpha$. However, the results and conclusions on the behavior of the flatband states as a function of the impurity strength are incomplete. In this Comment, I argue that because of the dispersionless nature of the flatband, the states spread out under the influence of a charged impurity forming a continuous band of states. I support my arguments with explicit numerical calculations which show the emergence of a continuum of states.

• Received 27 January 2020
• Revised 4 March 2020
• Accepted 6 May 2020

DOI:https://doi.org/10.1103/PhysRevB.101.197102