发表机构
Department of Physics Earth and Environmental Science, Technical University of Kenya（肯尼亚科技大学地球与环境科学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出Bethe-Salpeter框架证明对称性保护带内Fröhlich散射，质量不对称性通过相位扭转破坏该保护并增强声子重整化。
AI 中文摘要
激子与晶格振动的耦合通常通过唯象模型处理，这些模型人为地将长程Fröhlich相互作用与短程Holstein相互作用分开。最近的解析工作已确立，在离域极限下，Fröhlich散射被电子-空穴干涉所抑制。在此，我们提出一个模型空间Bethe-Salpeter框架，用于评估从扩展态到局域态交叉区域的激子-声子耦合。我们建立了包含性激子-声子耦合权重与排他性带内（保持内部状态）散射振幅之间的根本区别：前者可通过精确的完备性求和规则获得，无需对激发态求和；后者则控制低能退相干。我们证明了一个精确的对称性定理：对于具有相等电子和空穴质量的反演对称相对坐标哈密顿量，带内Fröhlich顶点恒等于零，从而保护激子免受低能极性声子散射的影响。当引入质量不对称性时，有限动量相对波函数获得复相位扭转，破坏了这种保护。通过分析长波极限，我们推导出一个受控的小$q$激活定律，表明带内顶点按$F_{00}(q) \propto \Delta q^2 \langle r^2 \rangle$标度，其中$\Delta$参数化质量不对称性。最后，我们计算了二阶极化子自能位移，并证明质量不对称性显著增强了声子 dressing，确认对称性定理直接支配激子的多体能量重整化。这些结果为理解极性半导体中长程与局域激子-声子耦合之间的竞争提供了严格的概念框架。
英文摘要
The coupling of excitons to lattice vibrations is typically treated via phenomenological models that artificially separate long-range Fröhlich and short-range Holstein interactions. Recent analytical work has established that, in the delocalized limit, Fröhlich scattering is suppressed by electron--hole interference. Here we present a model-space Bethe--Salpeter framework to evaluate exciton--phonon coupling across the extended-to-localized crossover. We establish a fundamental distinction between the \emph{inclusive} exciton--phonon coupling weight, obtainable via an exact completeness sum rule without summation over excited states, and the \emph{exclusive} intraband (internal-state-preserving) scattering amplitude that governs low-energy decoherence. We prove an exact symmetry theorem: for an inversion-symmetric relative-coordinate Hamiltonian with equal electron and hole masses, the intraband Fröhlich vertex vanishes identically, protecting the exciton from low-energy polar phonon scattering. When mass asymmetry is introduced, the finite-momentum relative wavefunction acquires a complex phase twist that breaks this protection. By analyzing the long-wavelength limit, we derive a controlled small-$q$ activation law showing that the intraband vertex scales as $F_{00}(q) \propto Δq^2 \langle r^2 \rangle$, where $Δ$ parameterizes the mass asymmetry. Finally, we compute the second-order polaron self-energy shift and demonstrate that mass asymmetry dramatically enhances phonon dressing, confirming that the symmetry theorem directly governs the many-body energy renormalization of the exciton. These results provide a rigorous conceptual framework for understanding the competition between long-range and local exciton--phonon coupling in polar semiconductors.
