Lying in between these two extremes are semimetals such as bismuth and graphite, which have tunable surface states that are interesting but remain underexplored. By contrast, in metals, the high charge-carrier density makes it difficult to observe and control surface states, as the bulk shunts the surface conductivity. For example, surface charge accumulation in semiconductors leads to distinct 2D subbands tunable by electrostatic gating. Our work shows a way in which 3D spectra can be controlled using the approach of 2D twistronics.Īt the surface of a crystal, its periodic lattice is interrupted, and surface states arise with wavefunctions exponentially decaying into the bulk of the crystal 25. 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. 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. Moreover, twistronics has been used to modify near-surface states at the interface between van der Waals crystals 23, 24. This twistronics approach has resulted in numerous previously undescribed physics, including strong correlations and superconductivity in twisted bilayer graphene 10, 11, 12, resonant excitons, charge ordering and Wigner crystallization in transition-metal chalcogenide moiré structures 13, 14, 15, 16, 17, 18 and Hofstadter’s butterfly spectra and Brown–Zak quantum oscillations in graphene superlattices 19, 20, 21, 22. 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, 2, 3, 4, 5, 6, 7, 8, 9.
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