Semiregular tessellation of electronic lattices in untwisted bilayer graphene under anisotropic strain gradients

Abstract Two-dimensional (2D) moiré superlattices have emerged as a versatile platform for uncovering exotic quantum phases, many of which arise in bilayer systems exhibiting Archimedean tessellation patterns such as triangular, hexagonal, and kagome lattices. Here, we propose a strategy to engineer semiregular tessellation patterns in untwisted bilayer graphene by applying anisotropic epitaxial tensile strain (AETS) along crystallographic directions. Through force-field and first-principles calculations, we demonstrate that AETS can induce a rich variety of semiregular tessellation geometries, including truncated hextille, prismatic pentagon, and brick-phase arrangements. Characteristic electronic Dirac and flat bands of the lattice models associated with these semiregular tessellations are observed near the Fermi level, arising from interlayer interactions generated by the spatial rearrangement of AB, BA, and SP domains. Furthermore, the real-space observations of electronic kagome, distorted Lieb, brick-like, and one-dimensional stripe lattices demonstrate that AETS enables tunable semiregular tessellation lattices. Our study identifies AETS as a promising new degree of freedom in moiré engineering, offering a reproducible and scalable platform for exploring exotic electronic lattices in moiré systems.