Spin Polarized and Valley Helical Edge Modes in Graphene Nanoribbons

TL;DR

This paper predicts and demonstrates the existence of spin-polarized, valley-helical edge modes in graphene nanoribbons with a bulk energy gap, which are robust against certain types of disorder, combining theoretical models and first-principles calculations.

Contribution

It introduces a new type of edge mode in graphene nanoribbons that are spin-polarized and valley-helical, protected by large momentum separation, supported by both tight-binding and first-principles methods.

Findings

Spin-polarized edge modes with valley index exist in gapped graphene nanoribbons.

These edge modes are helical and robust against smooth disorder.

The modes are confirmed by both tight-binding and first-principles calculations.

Abstract

Inspired by recent progress in fabricating precisely zigzag-edged graphene nanoribbons and the observation of edge magnetism, we find that spin polarized edge modes with well-defined valley index can exist in a bulk energy gap opened by a staggered sublattice potential such as that provided by a hexagonal Boron-Nitride substrate. Our result is obtained by both tight-binding model and first principles calculations. These edge modes are helical with respect to the valley degree of freedom, and are robust against scattering, as long as the disorder potential is smooth over atomic scale, resulting from the protection of the large momentum separation of the valleys.