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It is well known that amorphous solids display a phonon spectrum where theDebye $\sim \omega^2$ law at low frequency melds into an anomalous excess-modepeak (the boson peak) before entering a quasi-localized regime at higherfrequencies dominated by scattering. The microscopic origin of the boson peakhas remained elusive despite various attempts to put it in a clear connectionwith structural disorder at the atomic/molecular level. Using numericalcalculations on model systems, we show that the microscopic origin of the bosonpeak is directly controlled by the local breaking of center-inversion symmetry.In particular, we find that both the boson peak and the nonaffine softening ofthe material display a strong positive correlation with a new order parameterdescribing the local inversion symmetry of the lattice. The standardbond-orientational order parameter, instead, is shown to be a poor correlatorand cannot explain the boson peak in randomly-cut crystals with perfectbond-orientational order. Our results bring a unifying understanding of theboson peak anomaly for model glasses and defective crystals in terms of auniversal local symmetry-breaking principle of the lattice.

Local inversion-symmetry breaking controls the boson peak in glasses and crystals