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 moir\'e superlattices. Here we show that electronic states in three-dimensional (3D) crystals such as graphite can also be tuned by the superlattice potential arising 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 for near-surface 2D states whereas, in high magnetic fields, fractal states of Hofstadter's butterfly extend deep into graphite's bulk. Our work shows a venue to control 3D spectra by using the approach of 2D twistronics.
@article{arxiv.2211.16420,
title = {Mixing of surface and bulk electronic states at a graphite-hexagonal boron nitride interface},
author = {Ciaran Mullan and Sergey Slizovskiy and Jun Yin and Ziwei Wang and Qian Yang and Shuigang Xu and Yaping Yang and Benjamin A. Piot and Sheng Hu and Takashi Taniguchi and Kenji Watanabe and Kostya S. Novoselov and A. K. Geim and Vladimir I. Fal'ko and Artem Mishchenko},
journal= {arXiv preprint arXiv:2211.16420},
year = {2023}
}