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

Abstract

The moiré 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 moiré 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 ${\Phi }_0$.

6 pages, 4 figures

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Cited by in corpus (3)

• Band gap formation in commensurate twisted bilayer graphene/hBN moiré lattices
• Negative electronic compressibility in charge islands in twisted bilayer graphene
• Semimetallic and semiconducting graphene-hBN multilayers with parallel or reverse stacking