Universal classification of twisted, strained and sheared graphene moir\'e superlattices

TL;DR

This paper develops a universal framework for classifying various graphene moiré superlattices, based on high-precision microscopy and theoretical analysis, clarifying their crystallographic structures and electronic properties.

Contribution

It introduces a general formalism to classify all hexagonal moiré structures, resolving debates on their crystallography and providing detailed analysis of complex graphene superlattices.

Findings

Resolved small-angle twists and shears in graphene samples.

Identified large, complex moiré unit cells with non-trivial nanopatterns.

Developed a universal classification formalism for hexagonal moiré superlattices.

Abstract

Moir\'e superlattices in graphene supported on various substrates have opened a new avenue to engineer graphene's electronic properties. Yet, the exact crystallographic structure on which their band structure depends remains highly debated. In this scanning tunneling microscopy and density functional theory study, we have analysed graphene samples grown on multilayer graphene prepared onto SiC and on the close-packed surfaces of Re and Ir with ultra-high precision. We resolve small-angle twists and shears in graphene, and identify large unit cells comprising more than 1,000 carbon atoms and exhibiting non-trivial nanopatterns for moir\'e superlattices, which are commensurate to the graphene lattice. Finally, a general formalism applicable to any hexagonal moir\'e is presented to classify all reported structures.