Realizing a tunable honeycomb lattice in ABBA-stacked twisted double bilayer WSe$_2$

TL;DR

This paper proposes ABBA-stacked twisted double bilayer WSe$_2$ as a tunable platform for realizing a symmetric honeycomb lattice with controllable bandwidth, enabling exploration of correlated and topological quantum phases.

Contribution

It introduces a realistic, tunable moiré system with a symmetric honeycomb lattice, demonstrating control over electronic properties via twist angle and magnetic field, and explores emergent correlated phases.

Findings

Adjusting twist angle tunes bandwidth and hopping ratios.

In-plane magnetic field controls electronic structure and phase transitions.

Interaction-driven phases include canted antiferromagnetic insulator and charge-polarized insulator.

Abstract

The ideal honeycomb lattice, featuring sublattice and SU(2) spin rotation symmetries, is a fundamental model for investigating quantum matters with topology and correlations. With the rise of the moir\'e-based design of model systems, realizing a tunable and symmetric honeycomb lattice system with a narrow bandwidth can open access to new phases and insights. We propose the ABBA-stacked twisted double bilayer WSe$_2$ as a realistic and tunable platform for reaching this goal. Adjusting the twist angle allows the bandwidth and the ratio between hopping parameters of different ranges to be tuned. Moreover, the system's small bandwidth and spin rotation symmetry enable effective control of the electronic structure through an in-plane magnetic field. We construct an extended Hubbard model for the system to demonstrate this tunability and explore possible ordered phases using the Hartree-Fock approximation. We find that at a hole filling of $\nu = 2$ (two holes per moir\'e unit cell), an in-plane magnetic field of a few Tesla can ``dope" the system from a semimetal to a metal. Interactions then drive an instability towards a canted antiferromagnetic insulator ground state. Additionally, we observe a competing insulating phase with sublattice charge polarization. Finally, we discuss the experimental signatures of these novel insulating phases.