标题： 铜氧化物中激子的经典动力学和半经典分析 显示英文标题

标题： Classical dynamics and semiclassical analysis of excitons in cuprous oxide

摘要： 激子作为电子和空穴的束缚态，是固体状态中氢原子的类比，其量子谱在玻尔-索末菲原子模型的经典框架内得到解释。 在第一个类似氢的近似中，激子的光谱也由里德伯系列很好地描述，然而，由于周围晶体环境的影响，可以观察到与该系列的偏差。 对氧化亚铜中激子的理论处理需要包括晶体的能带结构，这导致量子谱中出现显著的精细结构分裂。 这是通过向系统中引入额外的自旋自由度来实现的，使得经典激子轨道在物理系统中的存在性和意义成为一个非平凡的问题。 最近，我们通过应用缩放技术并将经典动力学的能量固定为类似氢情况下主量子数 $n=5$ 对应的值，在氧化亚铜的量子力学重复光谱中直接揭示了周期性激子轨道的贡献 [J. Ertl 等，Phys. Rev. Lett. 129, 067401 (2022)]。 在这里，我们提出了氧化亚铜中激子的经典和半经典理论的全面推导。 特别是，我们研究了激子动力学的能量依赖性。 半经典和量子力学重复光谱都显示出随着能量降低，与类似氢行为的偏差更明显，这与自旋-轨道耦合的影响增大有关，因此激子轨道的长期运动速度更高。 半经典和量子力学激子重复光谱之间的一致性证明了经典和半经典方法在氧化亚铜激子中的有效性。 显示英文摘要

摘要： Excitons, as bound states of electrons and holes, embody the solid state analogue of the hydrogen atom, whose quantum spectrum is explained within a classical framework by the Bohr-Sommerfeld atomic model. In a first hydrogenlike approximation the spectra of excitons are also well described by a Rydberg series, however, due to the surrounding crystal environment deviations from this series can be observed. A theoretical treatment of excitons in cuprous oxide needs to include the band structure of the crystal, leading to a prominent fine-structure splitting in the quantum spectra. This is achieved by introducing additional spin degrees of freedom into the system, making the existence and meaningfulness of classical exciton orbits in the physical system a non-trivial question. Recently, we have uncovered the contributions of periodic exciton orbits directly in the quantum mechanical recurrence spectra of cuprous oxide [J. Ertl et al., Phys. Rev. Lett. 129, 067401 (2022)] by application of a scaling technique and fixing the energy of the classical dynamics to a value corresponding to a principle quantum number $n=5$ in the hydrogenlike case. Here, we present a comprehensive derivation of the classical and semiclassical theory of excitons in cuprous oxide. In particular, we investigate the energy dependence of the exciton dynamics. Both the semiclassical and quantum mechanical recurrence spectra exhibit stronger deviations from the hydrogenlike behavior with decreasing energy, which is related to a growing influence of the spin-orbit coupling and thus a higher velocity of the secular motion of the exciton orbits. The excellent agreement between semiclassical and quantum mechanical exciton recurrence spectra demonstrates the validity of the classical and semiclassical approach to excitons in cuprous oxide.