Motivated by recent experimental observations of size quantization of electron energy levels in graphene quantum dots \cite{ponomarenko} we investigate the level statistics in the simplest tight-binding model for different dot shapes by computer simulation. The results are in a reasonable agreement with the experiment which confirms qualitatively interpretation of observed level statistics in terms of "Dirac billiards" without taking into account many-body effects. It is shown that edge effects are in general sufficient to produce the observed level distribution and that even strong bulk disorder does not change the results drastically.
@article{arxiv.0804.2758,
title = {Electron energy level statistics in graphene quantum dots},
author = {H. De Raedt and M. I. Katsnelson},
journal= {arXiv preprint arXiv:0804.2758},
year = {2015}
}
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Published: Pis'ma v ZhETF, vol. 88, iss. 9, pp. 698 -- 701 (2008)