Probing the Hofstadter's butterfly in graphene/hexagonal-boron nitride moire superlattice using infrared magneto-spectroscopy*

Graphene on hexagonal boron nitride (hBN) exhibits a rotation-dependent moiré pattern. Perfect alignment causes the superlattice potential to match the magnetic length scale in graphene, yielding a butterfly-like energy spectrum. Infrared optical probes of cyclotron resonance can directly measure the associated energies by probing transitions across the fractal energy levels. We have fabricated high-quality monolayer graphene encapsulated with hBN, where the graphene layer forms a small twist angle of 0.5° with either the top or bottom hBN flake. The on-site energy difference results in the splitting of the valley-polarized zeroth Landau level creating a valley gap, where the periodicity of the moiré superlattice can modulate the gap size. For a rotational alignment of 0.5°, we measured the valley gap of approximately 12 meV using magneto-infrared spectroscopy. Additionally, we observed unusual broadening and splitting in the Landau level transitions at magnetic field below 6T, beyond what is typically observed in monolayer graphene. These phenomena are likely to arise from the fractal spectrum.