Graphene quantum dots: Beyond a Dirac billiard

TL;DR

This paper uses realistic simulations to study quantum confinement effects in graphene quantum dots, revealing deviations from ideal models and suggesting a way to characterize device roughness through energy level statistics.

Contribution

It provides detailed simulations of wavefunctions and energy levels in graphene quantum dots considering various disorder sources, highlighting deviations from simple Dirac billiard models.

Findings

Significant deviations from Dirac billiard predictions due to disorder.

Stable dependence of energy level spacing on edge roughness.

Potential method to characterize device roughness via Coulomb blockade measurements.

Abstract

We present realistic simulations of quantum confinement effects in ballistic graphene quantum dots with linear dimensions of 10 to 40 nm. We determine wavefunctions and energy level statistics in the presence of disorder resulting from edge roughness, charge impurities, or short-ranged scatterers. Marked deviations from a simple Dirac billiard for massless fermions are found. We find a remarkably stable dependence of the nearest-neighbor level spacing on edge roughness suggesting that the roughness of fabricated devices can be potentially characterized by the distribution of measured Coulomb blockade peaks.