3D to 2D localization in supertwisted multilayers

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 ${\mathbf{k}}_{\parallel }$ away from the $\mathrm{\Gamma }$ 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-André model and deduce the experimental signatures of 3D to 2D localization in transport experiments.