Visualizing lattice relaxation and strain fields in twisted bilayer graphene

Moiré superlattices, formed by stacking two-dimensional van der Waals layers with a slight lattice mismatch, have electronic band structures that are highly sensitive to structural changes, such as interlayer twist angle. For example, twisted bilayer graphene (TBG) exhibits unconventional superconductivity and ferromagnetism at a 'magic' interlayer twist angle of 1.1°, associated with formation of flat electronic bands. At the same time, lattice deformations, strain, and disorder can also dramatically influence the behavior observed in these systems. Visualizing the structure and strain fields of moiré materials is therefore paramount to understanding and controlling their emergent electronic behavior. In this talk, I will present work on the development of a technique termed Bragg interferometry, based on four-dimensional scanning transmission electron microscopy (4D-STEM), for directly and quantitatively mapping interlayer atomic displacements, structural relaxation, and strain fields in TBG. The results uncover two regimes of lattice relaxation in TBG based on twist angle, in contrast to previous models depicting one continuous process, as well as intrinsic nanoscale twist angle and strain disorder and unique striped strain phases arising from extrinsic uniaxial heterostrain. This work sheds light on structural changes underpinning the twist angle dependent electronic properties of TBG and provides a framework for visualizing lattice relaxation, disorder, and strain in other moiré materials.