Persistent currents in a graphene ring with armchair edges

TL;DR

This paper investigates persistent charge and spin currents in a graphene ring with armchair edges in the quantum spin Hall state, revealing how edge coupling and Rashba interaction influence these currents.

Contribution

It introduces a study of persistent currents in graphene rings considering edge states, inter-edge coupling, and Rashba effects, highlighting novel behaviors in QSH insulators.

Findings

Edge spin current approaches a finite value independent of ring radius.

Inter-edge coupling can open a Dirac gap and reduce persistent currents.

Rashba coupling can suppress persistent spin currents to zero at a critical point.

Abstract

A graphene nano-ribbon with armchair edges is known to have no edge state. However, if the nano-ribbon is in the quantum spin Hall (QSH) state, then there must be helical edge states. By folding a graphene ribbon to a ring and threading it by a magnetic flux, we study the persistent charge and spin currents in the tight-binding limit. It is found that, for a broad ribbon, the edge spin current approaches a finite value independent of the radius of the ring. For a narrow ribbon, inter-edge coupling between the edge states could open the Dirac gap and reduce the overall persistent currents. Furthermore, by enhancing the Rashba coupling, we find that the persistent spin current gradually reduces to zero at a critical value, beyond which the graphene is no longer a QSH insulator.