Quantum spin Hall phase in neutral zigzag graphene ribbons

TL;DR

This paper investigates the wavefunctions and spin properties of zero energy modes in zigzag graphene ribbons, demonstrating the conditions under which the quantum spin Hall phase emerges or is suppressed, influenced by ribbon width and spin-orbit interaction.

Contribution

It provides analytic expressions for wavefunctions and clarifies how intrinsic spin-orbit interaction affects the quantum spin Hall phase in zigzag graphene ribbons.

Findings

Odd-width ribbons are insulating and do not support QSH phase.

Intrinsic spin-orbit interaction enhances the energy gap in these systems.

Wavefunctions evolve with interaction strength and ribbon width.

Abstract

We present a detailed description of the nature of the wavefunction and spin distribution of the zero energy modes of zigzag graphene ribbons (ZGRs) in the presence of the intrinsic spin_orbit (I-SO) interaction. These states characterize the quantum spin Hall (QSH) phase in graphene ribbons. We provide analytic expressions for wavefunctions and show how these evolve as the strength of the interaction and the ribbon width are changed. For odd-width ribbons, we show that its insulating nature precludes the existence of a QSH phase. For these systems the I-SO interaction is predicted to have a stronger effect as shown by the enhancement of the gap as the interaction strength is turned on.