热核涨落对带隙重整化影响的光学表象
Optical representation of thermal nuclear fluctuation effect on band-gap renormalization
摘要：
由于核的动力学和量子涨落，绝缘材料的带隙被电子-声子相互作用以各种方式重整化。在微扰Allen-Heine-Cardona理论中，利用Fan-Migdal和Debye-Waller项的公式考虑了这些涨落效应。然而，在公式中材料依赖性不清楚。因此，在这项研究中，我们专注于德拜-沃勒项的分析形式，并发现该项可以使用动量矩阵重新表述。此外，光学选择规则被发现发挥作用。对于金刚石型材料，德拜-沃勒项可以近似地分解为光学跃迁能、原子核的均方位移和偶极跃迁几率的乘积。如我们的第一性原理计算所揭示的，分解也可以应用于锌-镍-型材料的附加近似。因此，在计算电子-声子相互作用之前，可以使用基本物理量来估计几种材料的德拜-沃勒项的大小。
英文摘要：
The bandgap of insulating materials is renormalized in various ways by the electron-phonon interaction owing to the dynamical and quantum fluctuations of nuclei. These fluctuation effects are considered in the perturbative Allen-Heine-Cardona theory using the formulae for the Fan-Migdal and Debye-Waller terms. However, the material dependence is not clear in the formulae. Thus, in this study, we focus on the analytical form of the Debye-Waller term and find that the term can be reformulated using the momentum matrix. In addition, the optical selection rule is found to play a role. For diamond-type materials, the Debye-Waller term can be approximately decomposed into a product of the optical transition energy, the mean square displacement of nuclei, and the dipole transition probability. The decomposition can also be applied with an additional approximation to zinc-blende-type materials, as revealed by our first-principles calculation. The magnitudes of the Debye-Waller term of several materials can thus be estimated using basic physical quantities prior to performing the calculation of the electron-phonon interaction.
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