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Van der Waals assembly enables exquisite design of electronic states in two-dimensional (2D) materials, often by superimposing a long-wavelength periodic potential on a crystal lattice using moiré superlattices. This twistronics approach resulted in a plethora of novel physics including strong correlations and superconductivity in twisted bilayer graphene, resonant excitons, charge ordering, and Wigner crystallisation in transition metal chalcogenide moiré structures, Hofstadter’s butterfly spectra and Brown-Zak quantum oscillations in graphene superlattices, to name but a few. Also, twistronics has been used to modify near-surface states at the interface between van der Waals crystals. 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. Such alignment is found to result in a multitude of 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 graphite’s bulk. Our work shows a venue to control 3D spectra by using the approach of 2D twistronics.

Rights:

• Creative Commons BY Attribution 4.0 International
  

Keyword: Van der Waals assembly, electronic states, moiré superlattices

Date published: 2023-08-24

Publisher: Springer Science and Business Media LLC

Journal:

• Nature (ISSN: 00280836) vol. 620 issue. 7975 p. 756-761

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Manuscript type: Publisher's version (Version of record)

MDR DOI:

First published URL: https://doi.org/10.1038/s41586-023-06264-5

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Updated at: 2025-02-23 22:48:16 +0900

Published on MDR: 2025-02-23 22:48:16 +0900