Inner and outer edge states in graphene rings: A numerical investigation

TL;DR

This study numerically explores how the geometry, edge symmetries, and corner structures of graphene rings influence their electronic properties, revealing the formation of edge state sub-bands and their coupling effects.

Contribution

It provides a detailed numerical analysis of edge state behaviors in various graphene ring geometries and edge terminations, highlighting the role of inner-outer edge interactions.

Findings

Inner edge states evolve differently under magnetic fields compared to outer edge states.

Formation of sub-bands of edge states separated by energy gaps due to anticrossings.

Coupling between inner and outer edge states causes anticrossings observed in charge density maps.

Abstract

We numerically investigate quantum rings in graphene and find that their electronic properties may be strongly influenced by the geometry, the edge symmetries and the structure of the corners. Energy spectra are calculated for different geometries (triangular, hexagonal and rhombus-shaped graphene rings) and edge terminations (zigzag, armchair, as well as the disordered edge of a round geometry). The states localized at the inner edges of the graphene rings describe different evolution as a function of magnetic field when compared to those localized at the outer edges. We show that these different evolutions are the reason for the formation of sub-bands of edge states energy levels, separated by gaps (anticrossings). It is evident from mapping the charge densities that the anticrossings occur due to the coupling between inner and outer edge states.