Quantitatively Mapping Relaxation in Moiré Superlattices Using Interferometric 4D-STEM

It is now well established that changing the relative orientation and/or lattice constant mismatch between vertically-stacked single atomic layers modulates emergent physicochemical behavior through the formation of moiré superlattices. However, the band structures and emergent physics of moiré materials are highly sensitive to spontaneous structural deformations, namely lattice relaxation (or “atomic reconstruction”) and resulting intrinsic strain fields, in addition to extrinsic/incidental heterostrain. While it is widely accepted that lattice reconstruction universally occurs in moiré superlattices with small twist angles, direct experimental information regarding the mechanics of the relaxation process and the manifestation of intralayer strain remains limited. This knowledge gap presents critical impediments for generating accurate models that would allow the rational design and interpretation of the electronic/optical/photonic behavior in these systems. To address this challenge, we have developed Bragg interferometry, an imaging methodology that translates intensity information from scanning transmission electron microscopy diffraction data into quantitative measurements of intralayer deformations in encapsulated moiré superlattices. This talk will cover insights into measurements of lattice relaxation in twisted bilayer and trilayer graphene, as well as moiré superlattices of transition metal dichalcogenides. The results of this work serve to deepen our understanding of fundamental structure–property relationships in moiré superlattices and provide a framework for leveraging structural distortions and strain as additional tuning knobs for modifying the unique (opto)electronic behavior of these structures.