Twistronic structures and moire superlattices in homo- & heterobilayers of transition metal dichalcogenides (TMDs)

We apply a multiscale modelling approach to study moiré superlattice in twisted homo- and heterobilayers of transition metal dichalcogenides (TMD), taking into account the interlayer hybridisation of the electronic orbital and lattice reconstruction due to stacking-dependent adhesion. First of all, we develop DFT-parametrized interpolation formulae for interlayer adhesion energies of TMDs with both parallel and antiparallel orientation of their unit cells and arbitrary offset of the honeycomb lattices in the adjacent layers. Then, we combine those interpolation formulae with elasticity theory and analyze the bilayer lattice relaxation into mesoscale domain structures. We find that 3R and 2H stacking domains develop for, respectively, bilayers with parallel (P) and antiparallel (AP) orientation of the monolayer unit cells, separated by a network of dislocations, for twist angles θ <θ_P∼2.5 and θ <θ_AP∼1. Such lattice reconstruction has been verified by STEM imaging. We also show that the triangular domain structures of P-oriented homobilayers would manifest itself in local tunnelling characteristics of marginally twisted bilayers: these domains feature the layer asymmetry of band-edge wave functions and also the ferroeletric interlayer polarisation. For AP bilayer, we show that the deformation of the lattices around domain walls (which resemble twist dislocations oriented along the planes of in bulk 2H crystals) generate piezo-electric charges at the junctions of the honeycomb domain wall network. Finally, we establish the electronic structure of the bilayer, taking into account the ferroelectric and piezolectric charge transfers.