激子效应存在时电子与声子间的细致平衡原理

中文摘要 AI 辅助

基于多体公式，我们推导了包含激子效应的电子-声子耦合，该耦合可保持电子与声子散射过程间的热力学细致平衡。我们从微观电子-原子核哈密顿量出发，在玻恩-奥本海默平衡几何附近展开，为电子和声子传播子构造有效作用量。从同一有效作用量出发，我们根据包含激子效应的非局域顶点$\boldsymbol{\textrm{G}}^{\boldsymbol{\textrm{s}}}$推导了电子和/or声子自能，该顶点推广了通常的局域相互作用顶点$\boldsymbol{g}^{\boldsymbol{\textrm{s}}}$。当电子和声子在屏蔽交换近似下是明确定义的准粒子，且$\boldsymbol{\textrm{G}}^{\boldsymbol{\textrm{s}}}$取静态极限时，两种自能均简化为包含相同$\boldsymbol{\textrm{G}}^{\boldsymbol{\textrm{s}}}$的费米黄金规则表达式，从而确保了细致平衡。作为应用，我们计算了石墨烯中的电子和声子线宽，并说明了该公共顶点构造。我们分析了由屏蔽交换能带结构引起的散射相空间减少，与激子效应导致的电子-声子顶点增强之间的竞争，发现顶点增强可以补偿并克服电子和声子线宽中的相空间减少。

英文摘要

Based on a many-body formulation, we derive an electron-phonon coupling including excitonic effects that preserves thermodynamic detailed balance between electronic and phononic scattering processes. We start from the microscopic electron-nucleus Hamiltonian, expand around the Born-Oppenheimer equilibrium geometry, and construct an effective action for the electronic and phononic propagators. From the same effective action, we derive both electronic and phononic self-energies in terms of a nonlocal vertex $\mathcal G^{\textrm{s}}$ including excitonic effects, which generalizes the usual local interaction vertex $g^{\textrm{s}}$. When electrons and phonons are well-defined quasiparticles in the screened-exchange approximation and $\mathcal G^{\textrm{s}}$ is taken in its static limit, both self-energies reduce to Fermi-golden-rule expressions containing the same $\mathcal G^{\textrm{s}}$, thereby ensuring detailed balance. As an application, we compute electronic and phononic linewidths in graphene and illustrate this common-vertex construction. We analyze the competition between the reduced scattering phase space induced by the screened-exchange band structure and the enhancement of the electron-phonon vertex due to excitonic effects, finding that the vertex enhancement can compensate for and overcome the phase-space reduction in both electronic and phononic linewidths.

发表机构

• Dipartimento di Fisica, Università di Roma La Sapienza（罗马大学物理系）
• Theory and Simulation of Materials (THEOS), and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院材料理论与模拟中心及国家计算设计与发现新材料中心）
• Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia（摩德纳与雷焦艾米利亚大学工程科学与方法系）

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