Phonon selection and interference in momentum-resolved electron energy loss spectroscopy

As momentum-resolved Electron Energy Loss Spectroscopy (q-EELS) becomes more widely used for phonon measurements, better understanding of the intricacies of the acquired signal is necessary. Selection rules limit the allowed scattering, which may prohibit the appearance of specific phonon branches in some measurements. Simultaneous sampling of the lattice across all basis atoms also warrants a coherent treatment of phonons, which yields a reciprocal-space repeating unit cell that is larger than the standard Brillouin zone. We thus introduce the concept of the ``interferometric Brillouin zone’’ where phonons are observed, which is closely related to the Dynamic Structure Factor. These effects follow from our new mathematical formalism for waves and vibrations, and we demonstrate calculations of q-EELS experiments using molecular dynamics and lattice dynamics. Results are compared to established q-EELS simulation methods in well-studied material systems, including the utilization of scattering selection rules to acquire a polarization-selective vibrational density of states. Finally, we note the analysis involved is directly applicable to any wave phenomena, such as plasmons or polaritons.

💡 Research Summary

The manuscript presents a comprehensive theoretical framework for interpreting momentum‑resolved electron energy‑loss spectroscopy (q‑EELS) measurements of phonons, emphasizing the role of selection rules and wave‑interference effects that have been largely overlooked in previous analyses. The authors begin by noting that modern q‑EELS instruments now possess sufficient energy and momentum resolution to probe phonon dispersions, vibrational densities of states (v‑DOS), and even topological phonon modes in nanostructured and defect‑rich materials. However, the raw spectra are shaped not only by the intrinsic phonon density of states but also by how the fast electron couples to the collective lattice vibrations.

To capture this coupling rigorously, the paper introduces a unified wave‑function formalism. Each phonon mode is represented by a complex vector Λ multiplied by a plane‑wave factor exp