Mixed Wannier-Bloch functions for electrons and phonons in periodic systems

We introduce mixed Wannier-Bloch functions for studying electronic and vibrational spectra of periodic systems. These functions carry both spatial localization and limited spectral broadening, thereby combining the advantages of descriptions based on energy eigenstates (Bloch states) and position eigenstates (Wannier states). For the analysis of vibrational modes, a lattice position operator is introduced, analogous to the electronic Berry-phase position operator. Application to vitreous SiO2 demonstrates that mixed Wannier-Bloch functions constitute a powerful tool for tracking fingerprints of short- and medium-range structural order in electronic and vibrational spectra.