Signatures of exciton orbits in quantum mechanical recurrence spectra of Cu$_2$O

TL;DR

This paper bridges quantum and classical descriptions of excitons in Cu2O by analyzing recurrence spectra, revealing how quantum peaks relate to classical exciton orbits, thus enhancing understanding of exciton behavior in semiconductors.

Contribution

It provides the first detailed comparison of quantum and semiclassical recurrence spectra of excitons, linking spectral features to classical exciton orbits in Cu2O.

Findings

Quantum recurrence spectra show peaks related to classical exciton orbits.

Classical exciton dynamics involve complex three-dimensional orbits.

Spectral analysis relates band-structure splittings to classical trajectories.

Abstract

The seminal work by T. Kazimierczuk et al. [Nature 514, 343 (2014)] has shown the existence of highly excited exciton states in a regime, where the correspondence principle is applicable and quantum mechanics turns into classical mechanics, however, any interpretation of exciton spectra based on a classical approach to excitons is still missing. Here, we close this gap by computing and comparing quantum mechanical and semiclassical recurrence spectra of cuprous oxide. We show that the quantum mechanical recurrence spectra exhibit peaks, which, by application of semiclassical theories and a scaling transformation, can be directly related to classical periodic exciton orbits. The application of semiclassical theories to exciton physics requires the detailed analysis of the classical exciton dynamics, including three-dimensional orbits, which strongly deviate from hydrogenlike Keplerian orbits. Our findings illuminate important aspects of excitons in semiconductors by directly relating the quantum mechanical band-structure splittings of excitons to the corresponding classical exciton dynamics.