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

TL;DR

This paper demonstrates how anisotropic epitaxial tensile strain can engineer semiregular tessellation patterns in bilayer graphene, leading to tunable exotic electronic lattices with potential for exploring new quantum phases.

Contribution

It introduces a method to create and control semiregular tessellations in bilayer graphene using anisotropic strain, expanding moiré engineering capabilities.

Findings

AETS induces various semiregular tessellations including truncated hextille and prismatic pentagon.

Electronic bands near the Fermi level are affected by interlayer interactions and stacking registry redistribution.

Real-space electronic lattices such as kagome and Lieb are tunable via AETS.

Abstract

Two-dimensional (2D) moir\'e 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. The characteristic electronic bands (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 redistribution of specific stacking registries (AB, BA, and SP). Furthermore, the electronic kagome, distorted Lieb, brick-like, and one-dimensional stripe lattices captured in real-space confirm the tunable nature of the semiregular tessellation lattices enabled by AETS. Our study identifies AETS as a promising new degree of freedom in moir\'e engineering, offering a reproducible and scalable platform for exploring exotic electronic lattices in moir\'e systems.