Twistraintronics: Designing Novel Electronic Structures with Twist and Strain

Over recent years, numerous experiments have reported the observation of unconventional superconductivity and strongly correlated phases of matter in superlattices formed by stacking two-dimensional materials. A prominent example is twisted bilayer graphene (TBG), where strong correlations emerge around the so-called "magic angle." These unique electronic properties are critically dependent on the moiré pattern of the superlattices. While two rotated graphene layers typically form hexagonal moiré patterns, experiments have revealed a diverse array of moiré geometries, often attributed to small strains in the samples. In this work, we demonstrate that the moiré patterns in these systems depend crucially on the interplay between twist and strain. We find that, with the right combination of twist angle and strain, it is possible to obtain practically any moiré pattern, even if the underlying layers are only slightly distorted. We identify specific conditions under which special moiré patterns emerge, including square, one-dimensional, and hexagonal patterns induced solely by strain. Moreover, we show that strain reshapes the moiré Brillouin zone, transforming it into a primitive cell that reflects the new geometry of the superlattice. The modification of moiré patterns leads to significant changes in the electronic properties of the system. Specifically, we find that in TBG strain tends to suppress the formation of flat bands, even in hexagonal patterns formed exclusively by strain. Finally, we discuss how these effects manifest in the continuum model and explore the potential role of electrostatic interactions. Our results offer a comprehensive description of the diverse moiré patterns observed in experiments and provide a robust theoretical foundation for engineering moiré structures with novel electronic properties.