Wannier Diagram and Brown-Zak Fermions of Graphene on Hexagonal Boron-Nitride

TL;DR

This paper presents a detailed simulation of magnetotransport in graphene on hBN, revealing Brown-Zak fermions and a complex Wannier diagram that explains various experimental features at the quantum level.

Contribution

It introduces a realistic simulation approach for magnetoconductance in graphene/hBN systems, including strain effects, and develops a novel Wannier diagram for Landau spectra.

Findings

Observation of Brown-Zak fermions at rational flux fractions

Analysis of Hofstadter butterfly using a new Wannier diagram

Explanation of spin and valley degeneracy lifting phenomena

Abstract

The moir\'e potential of graphene on hexagonal boron nitride (hBN) generates a supercell sufficiently large as to thread a full magnetic flux quantum $\Phi_0$ for experimentally accessible magnetic field strengths. Close to rational fractions of $\Phi_0$, $p/q \cdot\Phi_0$, magnetotranslation invariance is restored giving rise to Brown-Zak fermions featuring the same dispersion relation as in the absence of the field. Employing a highly efficient numerical approach we have performed the first realistic simulation of the magnetoconductance for a 250 nm wide graphene ribbon on hexagonal boron nitride using a full ab-initio derived parametrization including strain. The resulting Hofstadter butterfly is analyzed in terms of a novel Wannier diagram for Landau spectra of Dirac particles that includes the lifting of the spin and valley degeneracy by the magnetic field and the moir\'e potential. This complex diagram can account for many experimentally observed features on a single-particle level, such as spin and valley degeneracy lifting and a non-periodicidy in $\Phi_0$.