Dimensional reduction from Quasiperiodicity in 3D Supertwisted Spirals

Motivated by recent realizations of multilayer structures with continuously increasing twist angle (supertwisted spirals), we study the electronic properties of these systems near the Gamma point. The low-energy Hamiltonian of the system maps different in-plane momenta onto the Aubrey-Andre model, where the tunneling between layers competes with the quasi-periodic layer-dependent potential. The latter originates from the anisotropy of the band dispersion and the inter-layer twist. We demonstrate momentum-selective 3D-to-2D crossover, where the electrons with large in-plane momenta become highly localized in a small number of layers. On the contrary, the electrons with small momenta are delocalized among all the layers in the system. We discuss the experimental signatures of this phenomenon in doping-dependent transport experiments.