Hierarchical symmetry breaking in Moir\'e graphene domain-wall networks

TL;DR

This paper reveals how symmetry breaking in moiré graphene domain-wall networks leads to the spontaneous formation of chiral geometries, affecting electronic states and offering new control mechanisms in moiré bilayer systems.

Contribution

It introduces a comprehensive phase diagram of network morphologies driven by strain and flexibility, highlighting the emergence of chiral configurations through lattice relaxation.

Findings

Chiral network configurations are energetically favored under certain conditions.

Chiral networks alter the distribution of electronic states, shifting spectral weight to edge modes.

Network symmetry influences the localization of topologically protected boundary states.

Abstract

Moir\'e network formation in graphene bilayers breaks stacking symmetry, giving rise to domain walls that host topologically protected one-dimensional states. Here we show that these systems undergo an additional symmetry breaking at the level of the domain-wall network geometry, leading to the spontaneous emergence of chiral network configurations that are not determined by topology alone. Using atomistic structural relaxation and electronic-structure calculations, we show that TDW networks adopt chiral geometries through lattice relaxation. Via developing a comprehensive phase diagram defined by strain and interlayer flexibility, we discover three equilibrium network morphologies: straight, mono-chiral, and dual-chiral. Chiral networks arise from the global minimization of TDW energy under moir\'e geometric constraints. Tight-binding calculations show that straight networks host junction-centred states, whereas chiral networks shift spectral weight toward asymmetric edge modes. While topologically protected states naturally emerge at AB/BA domain boundaries in moir\'e bilayers, we demonstrated that the localization of boundary states is network-symmetry dependent. Our results show that symmetry breaking at both the stacking and network levels provides a new way to understand and control low-energy electronic states in moir\'e bilayers.