Disordered Crystals Reveal Soft Quasilocalized Glassy Excitations

Structural glasses formed by quenching a melt are known to host a population of low-energy quasilocalized (nonphononic) excitations whose frequencies ω follow a universal ∼ω^{4} distribution as ω→0, independently of the glass formation history, the interparticle interaction potential, or spatial dimension. Here, we show that the universal quartic law of nonphononic excitations also holds in disordered crystals featuring finite long-range order, which is absent in their glassy counterparts. We thus establish that the degree of universality of the quartic law extends beyond structural glasses quenched from a melt. We further find that disordered crystals, whose level of disorder can be continuously controlled, host many more quasilocalized excitations than expected based on their degree of mechanical disorder-quantified by the relative fluctuations of the shear modulus-as compared to structural glasses featuring a similar degree of mechanical disorder. Our results are related to glasslike anomalies experimentally observed in disordered crystals. More broadly, they constitute an important step toward tracing the essential ingredients necessary for the emergence of universal nonphononic excitations in disordered solids.