Topological Edge States Emerging from Twisted Moiré Bands

Abstract

We study twisted bilayer WSe${}_2$ within a continuum moiré 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 moiré 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 moiré-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 moiré materials.

11 pages, 6 figures