We propose twisted bilayers of certain group IV and IVB trigonal transition metal dichalcogenides (TMDs) MX2 (M=Zr, Hf, Sn and X=S, Se) as moir\'{e} materials. In monolayer form these TMDs have conduction band minima near the three inequivalent Brillouin zone M points and negligible spin-orbit coupling, implying six flavors of low-energy conduction band states. The flavor sectors decouple at the single-particle level and in twisted bilayers are accurately described by emergent moir\'e-periodic Hamiltonians that we derive from small-unit-cell density functional theory calculations. Because the valley-projected Hamiltonians have large valley-dependent mass anisotropies and are time-reversal invariant, spontaneous valley polarization is signaled in transport by anisotropy instead of by the anomalous Hall and magnetic circular dichroism signals commonly observed in graphene and K-valley TMD-based moir\'{e} multilayers.
@article{arxiv.2411.18828,
title = {Moir\'{e} band theory for M-valley twisted transition metal dichalcogenides},
author = {Chao Lei and Perry T. Mahon and Allan H. MacDonald},
journal= {arXiv preprint arXiv:2411.18828},
year = {2025}
}