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 superlattices1–9. This twistronics approach has resulted in numerous previously undescribed physics, including strong correlations and superconductivity in twisted bilayer graphene10–12, resonant excitons, charge ordering and Wigner crystallization in transition-metal chalcogenide moiré structures13–18 and Hofstadter’s butterfly spectra and Brown–Zak quantum oscillations in graphene superlattices19–22. Moreover, twistronics has been used to modify near-surface states at the interface between van der Waals crystals23,24. 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.