Interplay between symmetry and spin-orbit coupling in graphene nanoribbons

TL;DR

This paper investigates how symmetry and spin-orbit coupling influence the electronic properties of graphene nanoribbons, revealing curvature-induced spin splitting and edge effects that depend on ribbon geometry and symmetry.

Contribution

It provides a detailed analysis of the interplay between symmetry, curvature, and spin-orbit effects in graphene nanoribbons, highlighting differences between chiral and achiral configurations.

Findings

Curved ribbons exhibit spin-split bands due to broken inversion symmetry.

Flat ribbons with symmetric edges have spin-degenerate bands.

Chiral nanoribbons show enhanced edge coupling and size-dependent gaps.

Abstract

We study the electronic structure of chiral and achiral graphene nanoribbons with symmetric edges, including curvature and spin-orbit effects. Curved ribbons show spin-split bands, whereas flat ribbons present spin-degenerate bands. We show that this effect is due to the breaking of spatial inversion symmetry in curved graphene nanoribbons, while flat ribbons with symmetric edges possess an inversion center, regardless of their having chiral or achiral edges. We find an enhanced edge-edge coupling and a substantial gap in narrow chiral nanoribbons, which is not present in zigzag ribbons of similar width. We attribute these size effects to the mixing of the sublattices imposed by the edge geometry, yielding a distinct behavior of chiral ribbons from those with pure zigzag edges.