Graphene quantum dot on boron nitride: Dirac cone replica and Hofstadter butterfly

TL;DR

This paper investigates the electronic structure of graphene quantum dots on boron nitride under magnetic fields, revealing Dirac cone replicas and Hofstadter butterflies through large-scale simulations, highlighting the coexistence of relativistic and non-relativistic Landau levels.

Contribution

It demonstrates the unambiguous signature of Dirac cone replicas via the zeroth Landau level and butterfly, advancing understanding of moiré superlattice effects in graphene heterostructures.

Findings

Observation of Dirac cone replica via zeroth Landau level

Coexistence of relativistic and non-relativistic Landau levels

Identification of Hofstadter butterfly patterns

Abstract

Graphene flakes placed on hexagonal boron nitride feature in the presence of a magnetic field a complex electronic structure due to a hexagonal moir\'e potential resulting from the van der Waals interaction with the substrate. The slight lattice mismatch gives rise to a periodic supercell potential. Zone folding is expected to create replica of the original Dirac cone and Hofstadter butterflies. Our large-scale tight binding simulation reveals an unexpected coexistence of a relativistic and non-relativistic Landau level structure. The presence of the zeroth Landau level and its associated butterfly is shown to be the unambiguous signature for the occurrence of Dirac cone replica.