Moir\'{e} band theory for M-valley twisted transition metal dichalcogenides

TL;DR

This paper introduces a theoretical framework for twisted bilayers of certain transition metal dichalcogenides, revealing unique valley-dependent properties and potential for novel valleytronic applications.

Contribution

It develops emergent moiré Hamiltonians for M-valley TMD bilayers from first-principles calculations, highlighting valley polarization effects without magnetic signals.

Findings

Moiré materials with decoupled flavor sectors

Valley polarization manifests as transport anisotropy

Large valley-dependent mass anisotropies in Hamiltonians

Abstract

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 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.