High resolution study of the yellow excitons in Cu$_2$O subject to an electric field

TL;DR

This study uses high-resolution spectroscopy to analyze how external electric fields influence the exciton spectrum in Cu₂O, revealing complex spectral behavior and state mixing that challenge simple hydrogen-like models.

Contribution

It provides detailed experimental data and theoretical analysis of exciton behavior in Cu₂O under electric fields, highlighting the limitations of hydrogen models and the importance of anisotropy and spin-orbit effects.

Findings

Spectral lines are resolvable for n=3 to 5, enabling state identification.

Spectra depend strongly on light propagation and polarization configurations.

Electric fields induce mixing of states with different parity, activating dark states.

Abstract

We have used high resolution transmission spectroscopy to study the exciton level spectrum in Cu$_2$O subject to a longitudinal external electric field, i.e., in the geometry where the transmitted light is propagating along the field direction. Different experimental configurations given by the field orientation relative to the crystal and the light polarization have been explored. We focus on the range of small principal quantum numbers $n \leq 7$. The number of exciton states belonging to a particular principal quantum number increases with $n$, leading to an enhanced complexity of the spectra. Still, in particular for $n = 3 \ldots 5$ a spectral separation of the different lines is feasible and identification as well as assignment of the dominant state character are possible. We find a strong dependence of the spectra on the chosen light propagation direction and polarization configuration, reflecting the inadequacy of the hydrogen model for describing the excitons. With increasing the field excitonic states with different parity become mixed, leading to optical activation of states that are dark in zero field. As compared with atoms, due to the reduced Rydberg energy states with different $n$ can be brought into resonance in the accessible electric field strength range. When this occurs, we observe mostly crossing of levels within the experimental accuracy showing that the electron and hole motion remains regular. The observed features are well described by detailed calculations accounting for the spin-orbit coupling, the cubic anisotropy effects, and the symmetry-imposed optical selection rules.