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