Classical and semiclassical description of Rydberg excitons in cuprous oxide

TL;DR

This paper offers a semiclassical approach to understanding the fine-structure splitting of Rydberg excitons in cuprous oxide, linking classical dynamics with quantum energy levels.

Contribution

It introduces a semiclassical interpretation of excitonic fine-structure splitting using classical dynamics and adiabatic methods, extending beyond the hydrogen-like model.

Findings

Quasi-periodic motion on near-integrable tori observed

Semiclassical quantization matches quantum mechanical energy splittings

Adiabatic approach effectively describes exciton dynamics

Abstract

Experimental and theoretical investigations of excitons in cuprous oxide have revealed a significant fine-structure splitting of the excitonic Rydberg states caused by a strong impact of the valence band structure. We provide a semiclassical interpretation of that splitting by investigating the classical dynamics of the excitonic electron-hole pair beyond the hydrogen-like model. Considering the slow motion of Rydberg excitons in coordinate space compared to the fast dynamics of quasispin and hole spin we use an adiabatic approach and energy surfaces in momentum space for the computation of the exciton dynamics. We observe quasi-periodic motion on near-integrable tori. Semiclassical torus quantization yields the energy regions of the fine-structure splitting of $n$-manifolds in agreement with quantum mechanical computations.