We theoretically study a perpendicular electronic transport in twisted three-dimensional (3D) systems using the effective continuum model and the recursive Green’s function method [1].

The perpendicular electric conduction in twisted systems was probed in a recent experiment [2] while the transmission across the twisted interface has not been well examined theoretically. In this study, we develop a formulation for the electronic transport in the twisted 3D system, which is a pair of 3D materials stacked with a twist angle, by using the effective continuum model and recursive Green’s function method.

We apply the method to twisted graphite (rotationally-stacked graphite pieces), which is one of the simplest twisted 3D systems.

In the twisted graphite, we found that the perpendicular conductivity depends on the twist angle non-monotonously, and it cannot be explained by a simple picture based on the Fermi-surface overlap. We reveal that the anomalous twist-angle dependence is due to the Fano resonance by an interface-localized state, which is a remnant of the flat state of magic-angle twisted bilayer graphene. The existence of the interface-localized state is confirmed by calculating the local density of states using the recursive Green’s function method.

[1] T. Tani, T. Kawakami, M. Koshino, arXiv:2308.03993

[2] A. Inbar et al., Nature 614, 682 (2023).