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While often less emphasized than electronic properties, phonon spectral functions provide rich insight into quasiparticles and collective modes involving strong electron–phonon coupling. The hybridization between phonon branches and plasmons has recently been studied [1] to address the superconducting transition temperature in layered materials that host low-energy plasmon modes. Analysis of the phonon spectral function shows that nonadiabatic effects (beyond the Born–Oppenheimer approximation) may significantly enhance the stability of the superconducting phase.
In the dilute limit, the phonon spectral function provides valuable information about the nature of polaron formation. Two physically distinct contributions can be identified [2], both proportional to the polaron concentration: (i) an excess in phonon spectral weight (phonon production), associated with lattice deformation; and (ii) a redistribution of spectral weight toward lower frequencies (phonon softening). In contrast to systems with a finite concentration of itinerant charges, where softening primarily affects phonons at specific momenta, here the softening extends broadly across the Brillouin zone, reflecting the local character of the polaron lattice deformation.
[1] J. Krsnik, D. Novko, O. S. Barišić, Phys. Rev. B 110, L180505 (2024).
[2] O. S. Barišić, Phys. Rev. B 73, 214304 (2006).