3D to 2D localization in supertwisted multilayers

TL;DR

This paper investigates how electronic states in twisted multilayer 2D materials transition from three-dimensional to two-dimensional behavior as in-plane momentum increases, revealing a universal localization phenomenon.

Contribution

It introduces a universal 3D-to-2D transition in electronic states of twisted multilayers and maps this behavior to the Aubry-André model, providing experimental predictions.

Findings

States with high in-plane momentum are localized along the z axis.

States with low in-plane momentum are extended.

The transition can be observed in transport experiments.

Abstract

We study the electronic properties of multilayer "spirals" of two-dimensional materials with continuously increasing twist angle. The electronic states are shown to undergo a universal 3D-to-2D transition on increasing the in-plane momentum ${\bf k}_\parallel$ away from the $\Gamma$ point. The states with $k_\parallel>k_c$ are localized along the z axis due to mismatch between electronic dispersions of the twisted layers, whereas those with $k_\parallel<k_c$ are extended. We support our results by mapping of the system on the Aubry-Andr\'e model and deduce the experimental signatures of 3D to 2D localization in transport experiments.