Relaxation-driven flat bands and topology in moir\'e transition metal dichalcogenide heterobilayers

Abstract

Moir\'e transition metal dichalcogenide (TMD) heterobilayers are commonly modeled by a continuum theory that yields topologically trivial bands, in contrast to their homobilayer counterparts which host topological bands and fractional Chern insulators (FCI). We show this conclusion is an artifact of neglecting the pseudomagnetic field generated by lattice relaxation, an effect intrinsic to every moir\'e material. We develop a continuum model that resolves relaxation into three channels: a modified moir\'e potential with higher Fourier harmonics, a pseudoelectric (scalar deformation) potential, and a pseudomagnetic (vector) potential. Using WSe$_2$/WS$_2$ as a prototype, we find that the pseudomagnetic field alone gaps the third and fourth valence bands with Chern numbers $\pm 1$ over a broad range of twist angle and lattice mismatch, while the moir\'e potential correction and pseudoelectric potential narrow the bandwidth and enhance the bandgaps, which survive many-body interactions using neural-network variational Monte Carlo calculations. Relaxation also smoothens the Berry curvature and quantum metric relative to the rigid model, moving the band closer to the ideal Chern limit, beneficial for the quantum anomalous Hall effect, FCI states, and flat-band superconductivity when filled to higher bands. Our work establishes a new framework that connects first-principles calculations, through the continuum model, to many-body observables. Using this framework, we show moir\'e heterobilayers as a new class of topological materials whose topology is driven entirely by intrinsic lattice relaxation.