# Curvature-induced quantum spin-Hall effect on a M\"obius strip

## TL;DR

This paper demonstrates through numerical methods that a monolayer graphene M"obius strip exhibits a curvature-induced spin-Hall effect, highlighting the influence of topology on quantum spin transport.

## Contribution

It provides the first numerical evidence of a spin-Hall effect induced solely by the curvature and topology of a graphene M"obius strip.

## Key findings

- Curvature induces a spin-Hall current in graphene M"obius strips.
- Despite no Hall current, a spin-Hall effect naturally arises from topology.
- Symmetry considerations predict the existence of this effect.

## Abstract

The quantum Hall effect has been predicted and discovered in various condensed-matter systems. A promising quantum material for such topological effects is graphene. We report the numerical observation of a curvature-induced spin-Hall effect in a monolayer graphene M\"obius strip. The solution of the Dirac equation on the nontrivial and non-Euclidean manifold reveals that despite the absence of a Hall current, a spin-Hall current is a natural consequence for such a topology, as predicted from symmetry arguments.