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We propose a novel periodicity-free unfolding method of the electronic energyspectra. Our new method solves a serious problem that calculated electronicband structure strongly depends on the choice of the simulation cell, i.e.,primitive-cell or supercell. The present method projects the electronic statesonto the free-electron states, giving rise to the {\it plane-wave unfolded}spectra. Using the method, the energy spectra can be calculated as a completelyindependent quantity from the choice of the simulation cell. We have examinedthe unfolded energy spectra in detail for three models and clarified thevalidity of our method: One-dimensional interacting two chain model, monolayergraphene, and twisted bilayer graphene. Furthermore, we have discussed that ourpresent method is directly related to the experimental ARPES (Angle-ResolvedPhoto-Emission Spectroscopy) spectra.

Periodicity-free unfolding method of electronic energy spectra: Application to twisted bilayer graphene