Topological mosaics in moire superlattices of van der Waals heterobilayers

Van der Waals (vdW) heterostructures formed by twodimensional atomic crystals provide a powerful approach towards designer condensed matter systems1-15. Incommensurate heterobilayers with small twisting and/or lattice mismatch lead to the interesting concept of moire superlattices2-7, where the atomic registry is locally indistinguishable from commensurate bilayers but has local-to-local variation over long range. Here we show that such moire superlattices can lead to periodic modulation of local topological order in vdW heterobilayers formed by two massive Dirac materials. By tuning the vdW heterojunction from normal to the inverted type-II regime via an interlayer bias, the commensurate heterobilayer can become a topological insulator (TI), depending on the interlayer hybridization controlled by the atomic registry between the vdW layers. This results in a mosaic pattern of TI regions and normal insulator (NI) regions in moire superlattices, where topologically protected helical modes exist at the TI/NI phase boundaries. By using symmetry-based k . p and tight-binding models, we predict that this topological phenomenon can be present in inverted transition metal dichalcogenides heterobilayers. Our work points to a new means of realizing programmable and electrically switchable topological superstructures from two-dimensional arrays of TI nano-dots to one-dimensional arrays of TI nano-stripes.