一维、二维和三维材料中晶格动力学的一般不变性和平衡条件
General invariance and equilibrium conditions for lattice dynamics in 1D, 2D, and 3D materials
摘要：
振动模式的长波长行为在载流子输运、声子辅助光学性质、超导性以及材料的热机械和热电性质中起着核心作用。在这里，我们提出了一般的不变性和平衡条件的晶格势，这些允许恢复的二次色散的弯曲声子在低维材料中，与长波长弯曲模式的唯象模型。我们还证明，对于任何低维材料的弯曲模式可以有一个纯粹的平面外的偏振在真空方向和二次色散的长波长限制。此外，我们提出了一种有效的方法来处理不变性条件的晶体与非零玻恩有效电荷的长程偶极-偶极相互作用诱导的贡献的晶格势和应力张量。我们的方法被成功地应用到158个二维材料的声子色散，突出了其在低维材料的声子介导的性质的研究中的关键相关性。
英文摘要：
The long-wavelength behavior of vibrational modes plays a central role in carrier transport, phonon-assisted optical properties, superconductivity, and thermomechanical and thermoelectric properties of materials. Here, we present general invariance and equilibrium conditions of the lattice potential; these allow to recover the quadratic dispersions of flexural phonons in low-dimensional materials, in agreement with the phenomenological model for long-wavelength bending modes. We also prove that for any low-dimensional material the bending modes can have a purely out-of-plane polarization in the vacuum direction and a quadratic dispersion in the long-wavelength limit. In addition, we propose an effective approach to treat invariance conditions in crystals with non-vanishing Born effective charges where the long-range dipole-dipole interactions induce a contribution to the lattice potential and stress tensor. Our approach is successfully applied to the phonon dispersions of 158 two-dimensional materials, highlighting its critical relevance in the study of phonon-mediated properties of low-dimensional materials.
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