Dislocations in twistronic heterostructures

Long-period moiré superlattices at the twisted interface of van der Waals heterostructures relax into preferential stacking domains separated by dislocation networks. Here, we develop a mesoscale theory for dislocations in networks formed in twistronic bilayers with parallel (P) and antiparallel (AP) alignment of unit cells across the twisted interface. For P bilayers we find an exact analytical displacement field across partial dislocations and determine analytic dependences of energy per unit length and width on the orientation and microscopic model parameters. For AP bilayers we formulate a semi-analytical approximation for displacement fields across perfect dislocations, establishing parametric dependences for their widths and energies per unit length. In addition, we find regions in the parametric space of crystal thicknesses and Moiré periods for strong and weak relaxation of the Moiré pattern in multilayered twistronic heterostructures.