Decomposing electronic structures in twisted multilayers: Bridging spectra and incommensurate wave functions

The authors present here a unified theoretical framework for describing the electronic structure of twisted multilayer systems, including both commensurate and incommensurate cases. Their method decomposes physical observables into layer- and momentum-resolved contributions and introduces a low-rank Hamiltonian approximation for efficient computation. The framework is validated through calculations of spectral function and optical conductivity on moir\'e and quasicrystalline twisted bilayer graphene.