Theoretical modelling of phonon-polaritons in amorphous materials

The nature of bosonic excitations in disordered materials has remained elusive due to the difficulties in defining key concepts such as quasi-particles in the presence of disorder. We report on the experimental observation of phonon-polaritons in glasses, including a boson peak (BP), i.e. excess of THz modes over the Debye law. A theoretical framework based on the concept of diffusion is developed to model the broadening linewidth of the polariton due to disorder-induced scattering. It is shown that the scaling of the BP frequency with the diffusion constant of the linewidth strongly correlates with that of the Ioffe-Regel (IR) crossover frequency of the polariton. This result demonstrates the universality of the BP in the low-energy spectra of collective bosonic-like excitations in glasses, well beyond the traditional case of acoustic phonons, and establishes the IR crossover as the fundamental physical mechanism behind the BP.