Orbital quantization of electronic states in a magnetic field as the origin of second-harmonic generation in diamagnetic semiconductors

Abstract

Magnetic-field-induced second-harmonic generation (MFISH) has been studied in the III-V and II-VI diamagnetic semiconductors GaAs, CdTe, and (Cd,Mg)Te over broad spectral ranges and at temperatures varying from $6\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}200\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The external magnetic field gives rise to time-reversal symmetry breaking, causing optical nonlinearities. A series of narrow MFISH lines has been observed in the spectral range near the band gap in magnetic fields up to $11\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. The magnetoexciton states associated with the optical transitions between Landau levels are responsible for the observed MFISH spectra. Orbital quantization of electronic states is therefore established as an origin of MFISH generation. The rotational anisotropy of the MFISH signal distinctly differs from that in the electric-dipole approximation. Model calculations, based on a phenomenological analysis using nonlocal contributions to the nonlinear optical susceptibility, reveal the importance of nonlinear magneto-optical spatial-dispersion, which acts together with the electric-dipole term.