Polarization- and time-resolved nonlinear optical spectroscopy of excitons in Cu2O

Abstract

Excitons are Coulomb-bound states of a negatively charged electron in the conduction band and a positively charged hole in the valence band of a semiconductor or an insulator. Their hydrogen-like absorption spectrum was first detected in 1951 in cuprous oxide Cu2O. In 2014, a spectral scan using an ultra-narrow bandwidth laser extended the P exciton series in a natural Cu2O crystal to a principal quantum number of n = 25. This breakthrough opened up the field of Rydberg physics in semiconductors leading to numerous experimental and theoretical studies investigating their behavior in external fields as well as exciton-plasma and exciton-exciton interactions. The present study reports on second harmonic generation (SHG) spectroscopy of dark- and bright excitons in Cu2O. SHG is forbidden for laser light propagating along the high-symmetry [110] and [001] crystal axis. By applying a magnetic field up to 10 T perpendicular to the light direction, SHG becomes allowed due to the Zeeman- (ZE) and magneto-Stark effect (MSE). The polarization selection rules for both mechanisms are derived from point group theory considerations. The linear polarization angles of the incoming and outgoing light can be controlled in order to differentiate between both SHG mechanisms. The spin-forbidden dark paraexcitons are activated by admixture of the M = 0 component of the bright orthoexcitons in a magnetic field. The Rydberg series of dark paraexcitons up to a quantum number of n = 6 is detected using this method. Due to the electron-hole exchange interaction, the paraexcitons are generally located energetically below the orthoexcitons. This order is found to be reversed for the n = 2 state due to mixing of the yellow 2S orthoexciton with the green 1S orthoexciton. The blue series of excitons involves the same valence band as the yellow series but the second-lowest conduction band. Accessing these states using linear optical spectroscopy is challenging due to the high absorption in this spectral range. MSE and ZE-induced SHG has been shown to be a suitable investigation method enabling the detection of blue 1S, 2S, and 2P excitons and magneto-excitons up to n=8. By analyzing their magnetic-field shift and polariton effect, key properties of blue excitons, such as the resonance energies, the exciton radius, the band gap, the reduced exciton mass, and the anisotropic conduction band mass, are obtained. Difference frequency generation with two-photon excitation (2P-DFG) allows experimental investigations of excitons in the time domain. The pulses of the first laser induce a coherent exciton population by a two-photon excitation process. The pulses of the second laser stimulate the emission of photons with the energy difference between the excitons and the stimulating photons. By delaying the pulses of the second laser, the 2P-DFG signal is measured as a function of time. This technique is used to measure the coherence times of 1S and higher n excitons and magnetic-field-induced quantum beats of the three 1S orthoexciton states.