The vibrational energy of crystals is known to propagate in a fixed number of phonon branches allowed by symmetry. In the realm of nonlinear dynamics, however, additional nonlinear propagating modes are possible. Nonlinear propagating modes have unique properties that are important in many disciplines including optical communications, conducting polymers, biology, magnetism, and nuclear physics. Yet, despite the crucial importance of crystal lattice vibrations in fundamental and applied science, such additional propagating modes have not been observed in ordinary crystals. Here, we show that propagating modes exist beyond the phonons in fluorite-structured thoria, urania, and natural calcium fluoride using neutron scattering and first-principles calculations. These modes are observed at temperatures ranging from 5 K up to 1200 K, extend to frequencies 30–40% higher than the maximum phonon frequency, and travel at velocities comparable to or higher than the fastest phonon. The nonlinear origin of the modes is explained in part via perturbation theory, which approximately accounts for nonlinearity. Given that these modes are still clearly observed at 5 K, they are likely an inherent feature of the quantum ground state. The existence of these waves in three-dimensional crystals may have ramifications for material properties.

已知晶体的振动能在对称允许的固定数量的声子分支中传播。但是，在非线性动力学领域，可能会出现其他非线性传播模式。非线性传播模式具有独特的特性，这些特性在许多学科中都很重要，包括光通信，传导聚合物，生物学，磁性和核物理。然而，尽管晶格振动在基础科学和应用科学中至关重要，但是在普通晶体中还没有观察到这种额外的传播模式。在这里，我们使用中子散射和第一性原理计算表明，在萤石结构的氧化ria，尿素和天然氟化钙中，声子以外的传播模式存在。这些模式是在5 K至1200 K的温度范围内观察到的，扩展到比最大声子频率高30–40％的频率，并以与最快的声子相当或更高的速度行进。模态的非线性起源在某种程度上是通过扰动理论来解释的，该理论近似地说明了非线性。假设在5 K下仍能清晰观察到这些模式，则它们很可能是量子基态的固有特征。这些波在三维晶体中的存在可能会对材料性能产生影响。它们可能是量子基态的固有特征。这些波在三维晶体中的存在可能会对材料性能产生影响。它们可能是量子基态的固有特征。这些波在三维晶体中的存在可能会对材料性能产生影响。