Comment on "Fock-Darwin States of Dirac Electrons in Graphene-Based Artificial Atoms"

TL;DR

This paper critiques a previous study on graphene quantum dots, demonstrating that including both positive and negative energy states is essential for accurate energy level calculations, which affect optical spectra.

Contribution

It corrects prior calculations by emphasizing the importance of including negative energy basis states in modeling graphene quantum dots.

Findings

Including negative energy states alters the energy spectrum.

New energy levels appear in the optical spectrum.

Anticrossings occur between optical transition lines.

Abstract

Chen, Apalkov, and Chakraborty (Phys. Rev. Lett. 98, 186803 (2007)) have computed Fock-Darwin levels of a graphene dot by including only basis states with energies larger than or equal to zero. We show that their results violate the Hellman-Feynman theorem. A correct treatment must include both positive and negative energy basis states. Additional basis states lead to new energy levels in the optical spectrum and anticrossings between optical transition lines.