Magneto-Stark and Zeeman effect as origin of second harmonic generation of excitons in Cu2O

Abstract

We report on the experimental and theoretical investigation of magnetic-field-induced second harmonic generation (SHG) and two-photon absorption (TPA) of excited exciton states (n 3) of the yellow series in the cuprous oxide Cu2O. In this centrosymmetric material, SHG can occur due to constructive interplay of electric dipole and electric quadrupole/magnetic dipole transitions for light propagating along the low-symmetry directions [111] or [112]. By application of a magnetic field in Voigt configuration, SHG gets also allowed for excitation along the [110]-axis and even the high-symmetry cubic direction [001]. Combining a symmetry analysis and a microscopic theory, we uncover the two key contributions to the magnetic-field-induced SHG: the Zeeman effect and the magneto-Stark effect. We demonstrate systematic dependencies of the SHG intensity on the linear polarization angles of the ingoing fundamental laser and the outgoing SHG beam, complementary to the manuscript by Rommel et al. [1]. In general, the resulting contour plots in combination with a symmetry analysis allow one to determine uniquely the character of involved transitions. Moreover, we can separate in magnetic field the Zeeman and the magneto-Stark effect through appropriate choice of the experimental geometry and polarization configuration. We present a microscopic theory of the second harmonic generation of excitons in a centrosymmetric cubic semiconductor taking into account the symmetry and the band structure of cuprous oxide. Based on the developed microscopic theory we identify the main contributions to the second-order nonlinear susceptibility of S-, P -and D-excitons. We analyze the redistribution of SHG intensities between the excitonic states both in the absence and presence of the magnetic field and show good agreement with the experimental data. With increasing exciton principal quantum number the magneto-Stark effect overpowers the influence of the Zeeman effect. arXiv:2002.11560v1 [cond-mat.mes-hall]

Guide to optical spectroscopy of layered semiconductors

“…The SHG response of a material not only reflects the crystal structure but also depends on the electronic excitations 197 . The efficiency of the SHG signal can be enhanced by several orders of magnitude by selecting the excitation energy to be in resonance with excitonic states of the investigated materials 42 .…”

Semiconductor Rydberg Physics

“…Again we have tested this by SHG spectroscopy, for which we have chosen the optical axis to be parallel to the direction, along which no SHG is generated without magnetic field for symmetry reasons. Applying a magnetic field in Voigt configuration along the [110] crystal direction induces strong SHG signal, as can be seen from the spectra in Figure 22, [ 75,76 ] where the linear polarization of the fundamental light is chosen to be along the field and the polarization of the SHG light is rotated by 45° relative to it. The signal increases strongly with magnetic field and involves all states within a multiplet.…”

High resolution nanosecond spectroscopy of even-parity Rydberg excitons in Cu$_{2}$O

“…Recently, Mund et al [27][28][29][30] have studied even-parity excitonic states up to 9S using second-harmonic generation (SHG). In these experiments [27][28][29][30], broadband femtosecond pulses simultaneously excited a range of Rydberg states, and the resulting second harmonic was spectrally resolved using a monochromator.…”

“…Recently, Mund et al [27][28][29][30] have studied even-parity excitonic states up to 9S using second-harmonic generation (SHG). In these experiments [27][28][29][30], broadband femtosecond pulses simultaneously excited a range of Rydberg states, and the resulting second harmonic was spectrally resolved using a monochromator. Although cuprous oxide possesses inversion symmetry, SHG becomes allowed at exciton resonances when quadrupole terms are considered in the excitation or emission operators.…”