Twist and strain identification in moiré heterostructures

Abstract

The geometrical and electronic properties of moiré materials are highly sensitive to the twist and strain in the samples due to the moiré magnifying effect. Accurate identification of twist and strain in moiré materials is therefore essential. In this work, we establish a general framework to extract the twist and strain configurations from moiré images with either atomic or moiré scale resolution. With only moiré-wavelength information, we show that there is a continuous family of possible twist and strain configurations, each one accounting for different orientations of the moiré pattern. To estimate the most likely twist-strain configuration, we discuss additional constraints and methods involving the minimum elastic energy and the electronic spectra. The minimum elastic energy, in particular, reflects that shear configurations become much more favorable as the strain increases. As an example of the developed methodology, we discuss the formation and identification of strained triangular moiré patterns. Our framework provides a comprehensive approach to identify the twist and strain configurations in systems with moiré-scale resolution.