Delusive chirality and periodic strain pattern in moir\'{e} systems

Geometric phase analysis (GPA) is a widely used technique for extracting displacement and strain fields from scanning probe images. Here, we demonstrate that GPA should be implemented with caution when several fundamental lattices contribute to the image, in particular in twisted heterostructures featuring moir\'e patterns. We find that in this case, GPA is likely to suggest the presence of chiral displacement and periodic strain fields, even if the structure is completely relaxed and without distortions. These delusive fields are subject to change with varying twist angles, which could mislead the interpretation of twist angle dependent properties.