Helical networks in twisted bilayer graphene under interlayer bias

TL;DR

This paper demonstrates that in twisted bilayer graphene under interlayer bias, topologically protected helical modes form a network at the boundaries of gapped regions, enabling potential for customizable topological nanoelectronics.

Contribution

It reveals the formation of a topological helical network in biased twisted bilayer graphene and proposes methods to tailor it with valley-mixing adsorbates.

Findings

Helical modes appear at boundaries of gapped regions in biased twisted bilayer graphene.

A topological network of valley current vortices emerges, resembling the Chalker-Coddington network.

The network can be engineered by depositing valley-mixing adsorbates.

Abstract

A twisted graphene bilayer exhibits a triangular Moir\'e pattern in the local stacking, that smoothly alternates between the three basic types AA', AB' and BA'. Under an interlayer bias U, the latter two types develop a spectral gap, characterised by opposite valley Chern numbers. We show that for large enough Moir\'e periods and bias, these regions become depleted electronically, and topologically protected helical modes appear at their boundaries. This gives rise to a delocalised topological network of the Chalker-Coddington type, composed of valley current vortices. This network can be tailored by controlled deposition of valley-mixing adsorbates, which block transmission in selected links, thus opening the possibility of custom topological nanoelectronics.