论文标题
手性声子的能量分散理论
Theory of Energy Dispersion of Chiral Phonon
论文作者
论文摘要
我们已经开发了一种关于谐波近似中手性晶体中语音能量分散的微观理论。主要问题之一是关于用相反的``晶体''角动量的声音声子的声速分裂。我们已经表明，即使在手性晶体中，分裂也必须为零，并且差异从至少$ k^2 $或更高的能量分散体开始。对于手性光语音，分裂是显而易见的，我们为其$ k $ linear分割的公式提供了一种。另一个重要发现是关于微观模型中原子位移的可能相互作用。我们发现，$ \ Mathbf {d} _ {ij} \ cdot（\ MathBf {d} _i \ times \ times \ times \ times \ times \ times \ mathbf {d} _j）$的反对称性相互作用不允许在微观汉密尔顿（Chiral Phonons）中与Chiral Phonons中的微观汉密尔顿（Chiral Phonons）中的稳定性相对稳定。我们已经确定，声学和光学模式中的分裂源于$ g_ {u} $ - 类型对称的电动环形四极杆的谐波电位。这些约束对于建模真实材料很重要。我们的大多数微观计算都是针对（准）具有三角晶体对称性（包括TE）的一维系统进行的，但是这些结果通常也适用于其他手性声子系统。
We have developed a microscopic theory on phonon energy dispersion in chiral crystals within a harmonic approximation. One of the main issues is about the splitting of sound velocity of acoustic phonons with opposite ``crystal'' angular momentum. We have shown that the splitting must be zero even in chiral crystals and the difference starts from the order of at least $k^2$ or higher in their energy dispersion. Splitting is evident for chiral optical phonons, and we have derived a formula for their $k$-linear splitting. Another important finding is about possible interactions of atomic displacements in microscopic models. We have found that antisymmetric interactions of $\mathbf{D} _{ij} \cdot (\mathbf{d} _i \times \mathbf{d} _j) $ type are not allowed in microscopic Hamiltonians for chiral phonons in compatible with the stability against the Nambu-Goldstone mode. We have identified that the splitting in both acoustic and optical modes arises from the harmonic potentials with the electric toroidal quadrupole of $G_{u}$-type symmetry. These constraint are important for modeling real materials. Most of our microscopic calculations have been performed for (quasi-)one-dimensional systems with a trigonal crystal symmetry including Te, but these results generally hold also for other chiral phonon systems.
