The advent of monochromated electron energy-loss spectroscopy has enabled atomic-resolution vibrational spectroscopy, which triggered interest in spatially localized or quasi-localized vibrational modes in materials. Here we report the discovery of phonon vortices at heavy impurities in two-dimensional materials. We use density-functional-theory calculations for two configurations of Si impurities in graphene, Si–C₃ and Si–C₄, to examine atom-projected phonon densities of states and display the atomic-displacement patterns for select modes that are dominated by impurity displacements. The vortices are driven by large displacements of the impurities, and reflect local symmetries. Similar vortices are found at phosphorus impurities in hexagonal boron nitride, suggesting that they may be a feature of heavy impurities in crystalline materials. Phonon vortices at defects are expected to play a role in thermal conductivity and other properties.

中文翻译：

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二维材料中重杂质处的声子涡旋

单色电子能量损失光谱的出现使得原子分辨率振动光谱成为可能，这引发了人们对材料中空间局域或准局域振动模式的兴趣。在这里，我们报告了二维材料中重杂质处声子涡旋的发现。我们使用密度泛函理论计算石墨烯中 Si 杂质的两种构型 Si-C ₃和 Si-C ₄，以检查原子投影声子态密度并显示由杂质位移。涡流由杂质的大位移驱动，并反映局部对称性。在六方氮化硼中的磷杂质中也发现了类似的涡流，这表明它们可能是晶体材料中重杂质的特征。缺陷处的声子涡旋预计将在热导率和其他性能中发挥作用。