Rydberg excitons in cuprous oxide: A two-particle system with classical chaos

When an electron in a semiconductor gets excited to the conduction band the missing electron can be viewed as a positively charged particle, the hole. Due to the Coulomb interaction electrons and holes can form a hydrogen-like bound state called exciton. For cuprous oxide a Rydberg series up to high principle quantum numbers has been observed by Kazimierczuk et al. [Nature 514, 343 (2014)] with the extension of excitons up to the $\mu$m-range. In this region the correspondence principle should hold and quantum mechanics turn into classical dynamics. Due to the complex valence band structure of Cu$_2$O the classical dynamics deviates from a purely hydrogen-like behavior. The uppermost valence band in cuprous oxide splits into various bands resulting in a yellow and green exciton series. Since the system exhibits no spherical symmetry, the angular momentum is not conserved. Thus, the classical dynamics becomes non-integrable, resulting in the possibility of chaotic motion. Here we investigate the classical dynamics of the yellow and green exciton series in cuprous oxide for two-dimensional orbits in the symmetry planes as well as fully three-dimensional orbits. The analysis reveals substantial differences between the dynamics of the yellow and green exciton series. While it is mostly regular for the yellow series large regions in phase space with classical chaos do exist for the green exciton series.