Multiscale modelling of moiré systems: the case of transition metal dichalcogenides

  Recently, moiré superlattices (MS) from twisted bilayers of transition metal dichalcogenides (TB-TMDs) have gained great interest as a novel and robust platform for simulating quantum phases of matter on emergent 2D lattices^[1-8]. Unlike in twisted bilayer graphene, in TB-TMDs different sets of flat bands can be probed, depending on carrier type and density, chemical composition, twist angle and external fields. These flat bands can derive from states at the Γ point or at Κ/Κ' points in the Brillouin zone of the constituent monolayers, and the corresponding localised Wannier functions sit on sites of different lattices in real space, e.g., honeycomb (for Γ‐derived) or triangular (Κ/Κ'‐derived)^[9]. At small angles the moiré patterns exhibit periods of the order of a few nanometres, and the corresponding moiré unit cells can contain more than 10,000 atoms. From a computational perspective, accessing electronic structure properties of these small-angle systems is challenging because of the unfavourable scaling of standard first-principles techniques with system size. Here, I will present a novel ab initio tight binding method for twisted multilayers TMDs which enables to accurately describe the electronic structure of these systems taking into account atomic relaxation, chemical composition, spin-orbit coupling and external fields at a significantly reduced computational cost^[9]. Finally, I will present first-principles and classical Montecarlo calculations for a trilayer system, namely twisted MoSe₂ on a 2H-WSe₂ bilayer, in which both Γ‐derived and Κ/Κ'‐derived flat bands can be accessed by applying an external electric field. In this set-up it is possible to engineer correlated insulating states on different emerging lattices and study their interactions.

*Ref:
 ^[1] Wang L. et al., Nat. Mater. 19, 861-866 (2020)
 ^[2] Ghiotto A. et al., Nature 597, 345-349 (2021)
 ^[3] Regan E. C. et al, Nature 579, 359-363 (2020)
 ^[4] Xu Y. et al., Nature 587, 214-218 (2020)
 ^[5] Huang X. et al., Nat. Phys.17, 715-719 (2021)
 ^[6] Tang Y. et al., Nature 579, 535-538 (2020)
 ^[7] Kennes D. et al., Nat. Phys. 17, 155-163 (2021)
 ^[8] Li, T., Jiang, S., Shen, B. et al., Nature 600, 641-646 (2021)
 ^[9] Vitale et al., 2D mater. 8, 045010 (2021)