Moiré band theory for M-valley twisted transition metal dichalcogenides

We propose twisted bilayers of certain group IV and IVB trigonal transition metal dichalcogenides (TMDs) MX${}_2$ (M$=$Zr, Hf, Sn and X$=$S, Se) as moiré 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 moiré-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 moiré multilayers.