We investigate the optical excitation spectra and the photoluminescence depolarization dynamics in bilayer WS2. A different understanding of the optical excitation spectra in the recent photoluminescence experiment by Zhu et al. (arXiv:1403.6224) in bilayer WS2 is proposed. In the experiment, four excitations (1.68, 1.93, 1.99, and 2.37 eV) are observed and identified to be the indirect exciton for the Γ valley, trion, A exciton, and B exciton excitations, respectively, with the redshift for the A exciton energy measured to be 30∼50 meV when the sample synthesized from monolayer to bilayer. According to our study, by considering that there exist both the intralayer and charge-transfer excitons in the bilayer WS2, with interlayer hopping of the hole, there exists an excimer state composed by the superposition of the intralayer and charge-transfer exciton states. Accordingly, we show that the four optical excitations in the bilayer WS2 are the A charge-transfer exciton, A′ excimer, B′ excimer, and B intralayer exciton states, respectively, with the calculated resonance energies showing good agreement with the experiment. In our picture, the speculated indirect exciton, which involves a high-order phonon absorption/emission process, is not necessary. Furthermore, the binding energy for the excimer state is calculated to be 40 meV, providing reasonable explanation for the experimentally observed energy redshift of the A exciton. Based on the excimer states, we further derive the exchange interaction Hamiltonian. Then the photoluminescence depolarization dynamics due to the electron-hole exchange interaction is studied in the pump-probe setup by the kinetic spin Bloch equations. We find that there is always a residual photoluminescence polarization that is exactly half of the initial one, lasting for an infinitely long time, which is robust against the initial energy broadening and strength of the momentum scattering. This large steady-state photoluminescence polarization indicates that the photoluminescence relaxation time is extremely long in the steady-state photoluminescence experiment, and can be the cause of the anomalously large photoluminescence polarization, nearly 100%, observed in the experiment by Zhu et al. in the bilayer WS2. This steady state is shown to come from the unique form of the exchange interaction Hamiltonian, under which the density matrix evolves into the one which commutes with the exchange interaction Hamiltonian.
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