Multiphoton Polariton Spectroscopy on ZnO

Abstract

DiNerent nonlinear techniques are applied to investigate excitonic transitions from the upper valence bands (symmetry I-,, T9, r,) to the lowest conduction band (symmetry r7) in ZnO. Coherent techniques like three-photon difference frequency generation are used for resonances on the lower polariton branch, whereas incoherent techniques are well suited for the investigation on the upper polariton branch. Paraexcitons are detected without external perturbation. The angular dependence of the longitudinal transverse splitting is investigated by excitation of mixed-mode polaritons and analyzed with use of a suitable ansatz for the dielectric tensor in the classical wave equation. The isotropic point at 3.157 CV is studied by non-resonant second harmonic generation. Verschiedene nichtlineare Techniken werden angewandt, urn exzitonische Anregungen von den oberen Valenzbandern (Syrnmetrie r,, T9, r,) in das unterste Leitungsband (Symmetrie r,) in ZnO zu untersuchen. Koharente Techniken wie die Drei-Photonen-Differenzfrequenzerzeugung werden benutzt, urn Resonanzen auf dem unteren Polaritonast anzuregen, wahrend inkohirente Techniken fur Untersuchungen auf den oberen Polaritonasten geeignet sind. Paraexzitonen konnen ohne HuDere Storungen nachgewiesen wcrden. AuDerordentliche Polaritonen werden angeregt. Die Winkelabhlngigkeit der Longitudinal-Transversal LAufspaltung wird bestimmt und anhand eines geeigneten Ansatzes fur den dielektrischen Tensor beschrieben. Der isotrope Punkt bei 3,157 eV wird mit nichtresonanter Erzeugung der zweiten Harmonischen vermessen. ') Otto-Hahn-Str./PSF 500500, W-4600 Dortmund, Federal Republic of Germany.

Verification of $\boldsymbol{\Gamma}_{7}$ symmetry assignment for the top valence band of ZnO by magneto-optical studies of the free A exciton state

“…The controversy was first raised by Thomas [3] and Hopfield [4] by their pioneering reflectivity studies of excitonic transitions; they proposed that ZnO has a negative spin-orbit coupling, leading to a reversed 7 − 9 − 7 ordering. This reversed ordering is consistent with a wide variety of experimental data (see [5][6][7][8][9][10][11][12] for a few examples) and is also supported by first-principles calculations [13].…”

Unusual nonlinear strain dependence of valence-band splitting in ZnO

“…However, for any reasonable U e f f parameter, at zero strain, the crystal field splitting is always positive and the spin-orbit splitting is always negative because the p-d coupling in this system is significant and the positive contribution of the spin-orbit coupling due to oxygen p orbital is very small [19]. Therefore, the band order at the VBM should be Γ 7(6)v , Γ 9(6)v , Γ 7(1)v , in decreasing energy, in agreement with experiment results [25].…”

“…Because our calculated GGA values of ∆ CF and ∆ S O for equilibrium ZnO are 77 meV and -36 meV respectively, are much larger than the experimental results (41.7 meV and -8.0 meV) [25], one may question whether the density functional theory (DFT) is able to describe this phenomena correctly because it is known that DFT places the Zn 3d band at a too high energy, thus overestimates the p-d hybridization and incorrectly describe the splitting at the VBM. To test this, we use the so called LDA+U method [26] to adjust the position of the Zn 3d energy levels to be close to experimental values.…”

Valence-band-ordering of a strain-free bulk ZnO single crystal identified by four-wave-mixing spectroscopy technique

“…The excitons involved in the respective transitions are termed A-, B-, and C-excitons and abbreviated as X A , X B , and X C . Numerous reports have emerged over the past 50 years postulating either C 9 -symmetry [9][10][11][12][13][14][15][16][17][18] or C 7 -symmetry 1, [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] for the uppermost E 1 VB, as shown schematically on the right and left ends in Fig. 1(a), respectively.…”