Cloning of Dirac fermions in graphene superlattices

TL;DR

This paper demonstrates how aligning graphene with a boron nitride substrate creates superlattice minibands, revealing cloned Dirac points and enabling control over graphene's electronic properties through moire patterns.

Contribution

It provides experimental evidence of superlattice minibands and Dirac point cloning in graphene on boron nitride, advancing understanding of engineered electronic spectra in 2D materials.

Findings

Observation of second-generation Dirac points as resistivity peaks

Reversal of Hall effect indicating sign change of effective mass

Zak-type cloning of Dirac points under magnetic fields

Abstract

Lateral superlattices have attracted major interest as this may allow one to modify spectra of two dimensional electron systems and, ultimately, create materials with tailored electronic properties. Previously, it proved difficult to realize superlattices with sufficiently short periodicity and weak disorder, and most of the observed features could be explained in terms of commensurate cyclotron orbits. Evidence for the formation of superlattice minibands (so called Hofstadter's butterfly) has been limited to the observation of new low-field oscillations and an internal structure within Landau levels. Here we report transport properties of graphene placed on a boron nitride substrate and accurately aligned along its crystallographic directions. The substrate's moire potential leads to profound changes in graphene's electronic spectrum. Second-generation Dirac points appear as pronounced peaks in resistivity accompanied by reversal of the Hall effect. The latter indicates that the sign of the effective mass changes within graphene's conduction and valence bands. Quantizing magnetic fields lead to Zak-type cloning of the third generation of Dirac points that are observed as numerous neutrality points in fields where a unit fraction of the flux quantum pierces the superlattice unit cell. Graphene superlattices open a venue to study the rich physics expected for incommensurable quantum systems and illustrate the possibility to controllably modify electronic spectra of 2D atomic crystals by using their crystallographic alignment within van der Waals heterostuctures.