Topological Edge States Emerging from Twisted Moir\'e Bands

TL;DR

This paper introduces a continuum approach to study edge states in twisted bilayer WSe2, revealing tunable topological edge modes with potential for controlling boundary phenomena in moiré materials.

Contribution

A novel continuum method for analyzing boundary physics in topological moiré systems, overcoming previous limitations of momentum-space and lattice models.

Findings

Chiral edge modes are consistent with bulk Chern numbers.

Edge states are strongly localized and layer-polarized at the magic angle.

Displacement fields enable electrical control of topological transitions.

Abstract

We study twisted bilayer WSe$_2$ within a continuum moir\'e model and introduce a method for treating finite geometries directly in the continuum framework, overcoming limitations associated with momentum-space formulations and Wannier obstructions. By projecting a confinement potential onto bulk moir\'e eigenstates, we obtain a real-space description of edge physics without lattice models. Applying this approach to nanoribbons, we demonstrate chiral edge modes consistent with bulk Chern numbers and reveal their moir\'e-scale character. In the magic-angle regime, these states are strongly localized, exhibit layer-polarized counter-propagating modes, and are electrically tunable via a displacement field, enabling control of localization, hybridization, and topological transitions. Our results establish a general framework for boundary physics in topological moir\'e materials.