# Metallic Network of Topological Domain Walls

## TL;DR

This paper investigates the electronic and transport properties of a topological domain wall network, revealing semi-metallic behavior, quantized conductance, and potential applications in low-power quantum devices.

## Contribution

It provides a comprehensive analysis of electronic transport in topological domain wall networks, connecting theoretical predictions with experimental observations in twisted bilayer graphene.

## Key findings

- Network exhibits semi-metallic Dirac dispersion near charge neutrality.
- Quantized conductance observed in nanoribbons with sawtooth edges.
- Finite size effects induce a small energy gap in trident-edged ribbons.

## Abstract

We study the electronic and transport properties of a network of domain walls between insulating domains with opposite valley Chern numbers. We find that the network is semi-metallic with Dirac dispersion near the charge neutrality point and the corresponding electronic states distribute along the domain walls. Near the charge neutrality point, we find quantized conductance in nanoribbon with sawtooth domain wall edges that propagates along the boundaries and is robust against weak disorder. For a trident edged ribbon, we find a small energy gap due to the finite size effect making the nanoribbon an insulator. When the Fermi energy is away from charge neutrality point, all domain walls contribute to the conduction of current. Our results provide a comprehensive analysis of the electronic transport properties in a topological domain wall network that not only agrees qualitatively with experiments on marginally twisted bilayer graphene under a perpendicular electric field, but also can provide useful insights for designing low-power topological quantum devices.