Half-integer 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 φ₀ for experimentally accessible magnetic field strengths. Close to rational fractions of φ₀, 𝘱/𝘲·φ₀, 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 simulate the magnetoconductance of bulk graphene on hexagonal boron nitride. The resulting Hofstadter butterfly is analyzed in terms of a novel half-integer Wannier diagram for Landau spectra of Dirac particles. This complex diagram can account for many features observed in the simulation and in experiment on a single-particle level, such as spin and valley degeneracy lifting and a nonperiodicidy in φ₀.