Spectroscopic and temporal four-wave-mixing (FWM) measurements are carried out on a strain-free bulk ZnO single crystal, in order to clarify the valence-band-ordering. Under the collinearly polarized lights with the electric-field component parallel to the c-axis, which can excite dipole-allowed Γ 1-excitons, the FWM signal appears only in the energies corresponding to the B-exciton. Under the cross-linear polarization configuration exciting both Γ 5- and Γ 1-excitons, the FWM signal arising from the two-photon-coherence is absent in the energies corresponding to A-exciton. Both the results indicate that Γ 1-exciton state belongs exclusively to B-exciton, meaning that the valence-band ordering is Γ 9 - Γ 7 - Γ 7 in order of decreasing electron energy for the present strain-free ZnO single crystal.
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