Mixing of moiré-surface and bulk states in graphite

Abstract Van der Waals assembly enables the design of electronic states in two-dimensional (2D) materials, often by superimposing a long-wavelength periodic potential on a crystal lattice using moiré superlattices 1–9 . This twistronics approach has resulted in numerous previously undescribed physics, including strong correlations and superconductivity in twisted bilayer graphene 10–12 , resonant excitons, charge ordering and Wigner crystallization in transition-metal chalcogenide moiré structures 13–18 and Hofstadter’s butterfly spectra and Brown–Zak quantum oscillations in graphene superlattices 19–22 . Moreover, twistronics has been used to modify near-surface states at the interface between van der Waals crystals 23,24 . Here we show that electronic states in three-dimensional (3D) crystals such as graphite can be tuned by a superlattice potential occurring at the interface with another crystal—namely, crystallographically aligned hexagonal boron nitride. This alignment results in several Lifshitz transitions and Brown–Zak oscillations arising from near-surface states, whereas, in high magnetic fields, fractal states of Hofstadter’s butterfly draw deep into the bulk of graphite. Our work shows a way in which 3D spectra can be controlled using the approach of 2D twistronics.