# Coulomb effects on topological band inversion in the moir\'e of WSe$_2$/BAs heterobilayer

## TL;DR

This paper demonstrates how Coulomb interactions enable a large-gap, electrically tunable quantum spin Hall insulator in a WSe2/BAs heterobilayer, with potential applications in spintronics and topological electronics.

## Contribution

It reveals the role of Coulomb effects in inducing topological band inversion and large gaps in a moiré heterobilayer, advancing the understanding of tunable topological phases.

## Key findings

- Coulomb interactions shift conduction bands, enabling large-gap QSH states.
- Electric field induces band inversion in the heterobilayer.
- Moiré patterns lead to superstructures of QSH and excitonic insulators.

## Abstract

Quantum spin Hall (QSH) insulator with large gap is highly desirable for potential spintronics application. Here we realize electrically tunable QSH insulator with large gap in van der Waals heterobilayer of monolayer transition metal dichalcogenide (TMD) and hexagonal BAs. When the type II band alignment gets inverted in an electric field, the hybridization by interlayer hopping between the spin-valley locked valence band edges in TMD and the BAs conduction band edges leads to a stacking-configuration dependent topological band inversion. In the non-interacting limit, the double spin degeneracy of BAs leaves an un-hybridized conduction band inside the gap, so the heterobilayer is a spin-valley locked metal instead of a QSH insulator. With the Coulomb interaction accounted in the double-layer geometry, the interaction with the hybridization induced electric dipole shifts this un-hybridized conduction band upwards in energy, giving rise to a sizable global QSH gap. Consequently, this heterobilayer provides a platform for engineering electrically tunable QSH insulator with sizable band gap. In the long period moir\'e pattern with the spatial variation of local stacking-configurations, the competition between Coulomb interaction and interlayer hopping leads to superstructures of QSH insulators and excitonic insulators.