Robustness of edge states in graphene quantum dots

TL;DR

This paper investigates the stability and properties of edge states in disordered graphene quantum dots, demonstrating their proportionality to the dot's circumference and analyzing effects of symmetry-breaking perturbations.

Contribution

It provides an analytical and numerical study of edge states in disordered graphene quantum dots, including their quantity, energy shifts due to perturbations, and potential detection methods.

Findings

Edge states are proportional to the circumference over lattice constant.

Perturbations shift edge states away from zero energy but do not affect their total number.

Upper bound on magnetic moment of a graphene dot is established.

Abstract

We analyze the single particle states at the edges of disordered graphene quantum dots. We show that generic graphene quantum dots support a number of edge states proportional to circumference of the dot over the lattice constant. Our analytical theory agrees well with numerical simulations. Perturbations breaking electron-hole symmetry like next-nearest neighbor hopping or edge impurities shift the edge states away from zero energy but do not change their total amount. We discuss the possibility of detecting the edge states in an antidot array and provide an upper bound on the magnetic moment of a graphene dot.