Protected pseudohelical edge states in proximity graphene ribbons and flakes

TL;DR

This paper explores topological edge states in graphene with proximity-induced spin-orbit coupling, revealing pseudohelical states that are robust against scattering despite being topologically trivial.

Contribution

It introduces the concept of pseudohelical edge states in graphene with staggered intrinsic spin-orbit coupling, showing their protection and unique properties.

Findings

Pseudohelical edge states are protected against time-reversal scattering.

Edge states exhibit zero g-factor and carry finite spin current.

Robustness of edge states demonstrated on finite graphene flakes.

Abstract

We investigate topological properties of models that describe graphene on realistic substrates which induce proximity spin-orbit coupling in graphene. A $\mathbb{Z}_2$ phase diagram is calculated for the parameter space of (generally different) intrinsic spin-orbit coupling on the two graphene sublattices, in the presence of Rashba coupling. The most fascinating case is that of staggered intrinsic spin-orbit coupling which, despite being topologically trivial, $\mathbb{Z}_2 = 0$, does exhibit edge states protected against time-reversal scattering for zigzag ribbons as wide as micrometers. We call these states pseudohelical as their helicity is locked to the sublattice. The spin character and robustness of the pseudohelical modes is best exhibited on a finite flake, which shows that the edge states have zero $g$-factor, carry a finite spin current in the crossection of the flake, and exhibit spin-flip reflectionless tunneling at the armchair edges.