Theory of optical excitation spectra and depolarization dynamics in bilayerWS2from the viewpoint of excimers

Abstract

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 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 there exist both the intra-layer and charge-transfer excitons in the bilayer WS2, with inter-layer hopping of the hole, there exists excimer state composed by the superposition of the intra-layer 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 intra-layer 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 extremely 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.

On Valence-Band Splitting in Layered MoS2

“…7 Reducing the layer separation, by increasing number of layers, can improve the interlayer hopping and coupling, 43 which is indeed observed in Figure 4 with VBM splitting energies around 175 meV for 3L to 5L below 100 K. At high temperatures, the VBM splitting energy approaches that of 2L. Thermal expansion can effectively decouple adjacent layers by increasing interlayer spacing and reducing interlayer interaction and scattering.…”

van der Waals Metal‐Organic Framework as an Excitonic Material for Advanced Photonics

“…Therefore, 3.4 eV bandgap of 1 should provide high exciton binding energies of 0.45 and 0.2 eV. These estimated values are typical for layered crystals while the full width at half‐maximum (FWHM) of exciton lines (19 and 36 nm) is compared to that of pure organic and inorganic 2D crystals at room temperature. Using the lattice parameters of 1 (Figure S1, Supporting Information) we also estimated the minimal radii of excitons proposed: ≈4.8 Å for the interlayer and ≈9.5 Å for the intralayer ones, which are consistent values for excitons in van der Waals crystals .…”

Coupling and Interlayer Exciton in Twist‐Stacked WS2 Bilayers

“…It would be interesting to be able to control the growth of different twist angles, for example, by tuning the growth temperature and precursor concentration, which will be our future study. Twisted TMDs bilayer is good platform to study many-body phenomenon, such as interlayer exciton [ 6,21 ] and trion. [ 22 ] Due to the spin and layer pseudospin coupling in TMDs AB stacking bilayer, interlayer hopping energy is twice of spin-orbital coupling (SOC) strength.…”