Electron energy level statistics in graphene quantum dots

TL;DR

This paper investigates electron energy level statistics in graphene quantum dots using tight-binding simulations, confirming experimental observations and highlighting the role of edge effects over bulk disorder.

Contribution

It provides the first detailed computational analysis of level statistics in graphene quantum dots, emphasizing edge effects and their sufficiency in explaining experimental results.

Findings

Level statistics agree with experimental data.

Edge effects are crucial in determining level distribution.

Bulk disorder does not significantly alter the results.

Abstract

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.