Fig. 5. Schematic of donor bound dark excitons and spin state initialization.

a Top is a schematic of the spin-valley coupled band edges. Green and brown lines denote electron (hole) spin pointing up (down) and down (up), respectively. Dashed lines indicate a shallow donor level, where carrier’s spin-valley locked index is preserved in the relatively smooth trapping potential. Bottom cartoon illustrates the donor configuration D where an electron (blue circle) is trapped by a positive charge center. Under σ+ polarized resonant excitation of free intervalley trion $X_T^{-}$, b the formation of $X_T^{-}$ (top cartoon) depletes the donor electron spins in K′ valley. This results in optical orientation of spin and valley polarized electron coupled to the shallow donor (bottom cartoon, D_K,↓). D_K,↓ can then capture a neutral dark exciton in the opposite valley, c, forming a donor bound dark exciton $D{X}_d^{K\prime }$. $D{X}_d^{K\prime }$ can emit light via defect assisted direct electron-hole recombination (peak S1), or via coupling to the bright trion assisted by phonons, which are by either emitting valley conserved but electron spin flipped Γ₅ phonon (peak S3), or emitting electron spin conserved but valley flipped K₂ phonon (peak S2). The opposite hole valley configuration of $X_T^{-}$ and $D{X}_d^{K\prime }$ dictates that the emitted light of $D{X}_d^{K\prime }$ is σ- polarized and opposite to that of excitation. d, e illustrates the scenario of resonant excitation of free intravalley $X_S^{-}$, which depletes spin down electrons of donor in the same valley. The donor bound dark exciton formed then has the same hole valley configuration, and emit light of the same circular polarization as the excitation. See text for details. Note that the schematics used here are based on single particle picture, for the convenience of explaining spin, valley, and charge degrees of freedom of the quasiparticles, and the stokes process with different phonons.