Recent developments in experiments with vibrational electron energy loss spectroscopy (EELS) have revealed spectral shape variations at spatial resolutions down to sub-atomic scale. Interpretation in terms of local phonon density of states enables their qualitative understanding, yet a more detailed analysis is calling for advances in theoretical methods. In Zeiger and Rusz, Phys. Rev. Lett. 124, 025501 (2020) we have presented a frequency resolved frozen phonon multislice method for simulations of vibrational EELS. Detailed simulations for a plane wave electron beam scattering on a vibrating hexagonal boron nitride are presented in a companion manuscript (Zeiger and Rusz, arXiv:2104.03197). Here we present simulations of vibrational EELS assuming a convergent electron probe of nanometer size and atomic size on a hexagonal boron nitride structure model with a planar defect. With a nanometer beam we observe spectral shape modifications in the presence of the defect, which are correlated with local changes of the phonon density of states. With an atomic size electron beam, we observe the same, although with better contrast. In addition, we observe atomic level contrast and sub-atomic scale spectral shape modifications, which are particularly strong for small detector collection angles.
A lattice dynamical treatment for the total potential energy of single-walled carbon nanotubes and its applications: relaxed equilibrium structure, elastic properties, and vibrational modes of ultra-narrow tubes
在本文中，我们提出了一个晶格动力学处理的总势能为单壁碳纳米管（SWCNT的），除了一个参数的非线性效应，从平面石墨烯片的振动能提取。在此基础上，我们系统地研究了单壁碳纳米管的弛豫晶格构型、应变能、杨氏模量和泊松比以及弛豫平衡小管结构的晶格振动特性。我们对各种物理量的计算结果与现有的实验测量结果很好地一致。特别是，我们证实了弛豫效应使键长变长，各种光学振动模式的频率变软;我们的计算提供了扶手椅管的杨氏模量超过平面石墨烯片的证据，并且杨氏模量和泊松比的大直径极限与石墨的实验值一致;对直径在0.2 ~ 0.5nm范围内的超窄管径向呼吸模式的计算结果与实验结果和已有的{ \it ab initio}计算结果吻合较好;对于直径为2nm的细管，计算的小管切平面光学模和径向呼吸模的频率也与实验测量值符合得很好。此外，我们的计算表明，松弛的单壁碳纳米管的各种物理量实际上可以根据为相应的理想单壁碳纳米管定义的手性角来扩展。
Emergence and suppression of phonon vortices in two-dimensional crystals: Interplay of lattice symmetry, heavy impurities, and shear
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Physics and Information Technology, Shaanxi Normal University（陕西师范大学物理学与信息技术学院）；Center for Theoretical Interdisciplinary Sciences, Wenzhou Institute, University of Chinese Academy of Sciences（中国科学院大学温州研究院交叉科学中心）
