We calculate the scattering rates of phonons on two-level systems in disordered trigonal and hexagonal crystals. We apply a model in which the two-level system, characterized by a direction in space, is coupled to the strain field of the phonon via a tensor of coupling constants. The structure of the tensor of coupling constants is similar to the structure of the tensor of elastic stiffness constants, in the sense that they are determined by the same symmetry transformations. In this way, we emphasize the anisotropy of the interaction of elastic waves with the ensemble of two-level systems in disordered crystals. We also point to the fact that the ratio $γ_l/γ_t$ has a much broader range of allowed values in disordered crystals than in isotropic solids.
We investigate the effect of spatially correlated disorder on the Anderson transition of phonons in three dimensions using a Greens function based approach, namely, the typical medium dynamical cluster approximation (TMDCA), in mass-disordered systems. We numerically demonstrate that correlated disorder with pairwise correlations mitigates the localization of the vibrational modes. A correlation driven localization-delocalization transition can emerge in a three-dimensional disordered system with an increase in the strength of correlations.
Among the many physical properties, the amorphous state manifests itself in the most spectacular way in heat transport. Anomalously low thermal conductivity, its low-temperature dependence as a function of temperature, the presence of a plateau of thermal conductivity, all are definitely different when compared with the ordered state of crystals. For this reason, the microscopic mechanisms from which these surprising behaviors may emerge have been the subject of intensive theoretical research and even more extensive experimental research. These investigations have led to the detection of a hug…
Hybrid quantum-classical matrix-product state and Lanczos methods for electron-phonon systems with strong electronic correlations: Application to disordered systems coupled to Einstein phonons
Georg-August-Universität Göttingen（哥廷根大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
Electron-phonon mediated heat flow in disordered graphene
我们计算的热通量和电子-声子热导在一个无序的石墨烯片，超越了费米的黄金法则的方法，充分考虑到修改的电子-声子相互作用的无序。在$k_F l >> 1$（其中$k_F$是费米波矢，l是平均自由程）体系中，采用Keldysh方法结合标准杂质平均法，我们同时考虑了电子与声子之间的标量势（即形变势）和矢量势耦合。我们还考虑了电子屏蔽的影响，在费米能级。我们发现，热通量和热导率的温度依赖性是敏感的无序和屏蔽的存在下，并反映了潜在的手性性质的电子在石墨烯和相应的修改其扩散行为。在弱屏蔽的情况下，无序增强了清洁系统的低温热通量（将相关幂律从$T^4$变为$T^3$），并且变形势占主导地位。对于强屏蔽，变形势和矢量势耦合的贡献相当，低温热流服从$T^5$幂律。
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 $\sim\!ω^4$ distribution as $ω\!\to\!0$, 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 structu…
We derive exact results for the fluctuations in energy produced by microscopic disorder in near-crystalline athermal systems. Our formalism captures the heterogeneity in the elastic energy of polydispersed soft disks in energy-minimized configurations. We use this to predict the distribution of interaction energy between two defects in a disordered background. We show this interaction energy displays an average power-law behaviour $\langle δE \rangle \sim Δ^{-4}$ at large distances $Δ$ between the defects. These interactions upon disorder average also display the sixfold symmetry of the underl…
We study jammed near-crystalline materials composed of frictionless spheres in three dimensions. We analyze the fluctuations in positions and forces produced by small polydispersity in particle sizes. We generalize a recently developed perturbation expansion about the crystalline ordered state to three dimensional systems. This allows us to exactly predict changes in positions and forces as a response to the changes in particle radii. We show that fluctuations in forces orthogonal to the lattice directions are highly constrained as compared to the fluctuations along lattice directions. Additio…
