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Dark trions and biexcitons in WS 2 and WSe 2 made bright by e-e scattering

View Article: PubMed Central - PubMed

ABSTRACT

The direct band gap character and large spin-orbit splitting of the valence band edges (at the K and K’ valleys) in monolayer transition metal dichalcogenides have put these two-dimensional materials under the spot-light of intense experimental and theoretical studies. In particular, for Tungsten dichalcogenides it has been found that the sign of spin splitting of conduction band edges makes ground state excitons radiatively inactive (dark) due to spin and momentum mismatch between the constituent electron and hole. One might similarly assume that the ground states of charged excitons and biexcitons in these monolayers are also dark. Here, we show that the intervalley (K ⇆ K′) electron-electron scattering mixes bright and dark states of these complexes, and estimate the radiative lifetimes in the ground states of these “semi-dark” trions and biexcitons to be ~10 ps, and analyse how these complexes appear in the temperature-dependent photoluminescence spectra of WS2 and WSe2 monolayers.

No MeSH data available.


Intervalley electron-electron scattering process.Schematics of the band structures of WX2 near the K, K′ points of the BZ, and the intervalley scattering process that mixes dark and bright states of trions (T) and biexcitons (B). Eg is the band gap and ΔSO stands for the conduction band spin splitting. Due to the large spin-orbit splitting in the valence band, the valence band is shown only for the higher-energy spin-polarised states.
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f1: Intervalley electron-electron scattering process.Schematics of the band structures of WX2 near the K, K′ points of the BZ, and the intervalley scattering process that mixes dark and bright states of trions (T) and biexcitons (B). Eg is the band gap and ΔSO stands for the conduction band spin splitting. Due to the large spin-orbit splitting in the valence band, the valence band is shown only for the higher-energy spin-polarised states.

Mentions: Applying the spin and valley selection rules to ground state trions and biexcitons might imply that these charge complexes are dark, too. In the ‘dark’ (d) state both electrons are in the bottom spin-orbit split states of c-band, whereas in the state to be ‘bright’ (b), one of the electrons has to be in the excited spin-split state. Here, we show that an intervalley scattering2021 of the c-band electrons mixes dark and bright states of complexes (Fig. 1), hence transferring some optical strength from b- to d-states and making dark state ‘semi-dark’. For the resulting recombination line of such semi-dark complexes, we find that it is shifted downwards in energy (relative to the bright trion line) by 2ΔSO, twice the c-band spin-orbit splitting.


Dark trions and biexcitons in WS 2 and WSe 2 made bright by e-e scattering
Intervalley electron-electron scattering process.Schematics of the band structures of WX2 near the K, K′ points of the BZ, and the intervalley scattering process that mixes dark and bright states of trions (T) and biexcitons (B). Eg is the band gap and ΔSO stands for the conduction band spin splitting. Due to the large spin-orbit splitting in the valence band, the valence band is shown only for the higher-energy spin-polarised states.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5382684&req=5

f1: Intervalley electron-electron scattering process.Schematics of the band structures of WX2 near the K, K′ points of the BZ, and the intervalley scattering process that mixes dark and bright states of trions (T) and biexcitons (B). Eg is the band gap and ΔSO stands for the conduction band spin splitting. Due to the large spin-orbit splitting in the valence band, the valence band is shown only for the higher-energy spin-polarised states.
Mentions: Applying the spin and valley selection rules to ground state trions and biexcitons might imply that these charge complexes are dark, too. In the ‘dark’ (d) state both electrons are in the bottom spin-orbit split states of c-band, whereas in the state to be ‘bright’ (b), one of the electrons has to be in the excited spin-split state. Here, we show that an intervalley scattering2021 of the c-band electrons mixes dark and bright states of complexes (Fig. 1), hence transferring some optical strength from b- to d-states and making dark state ‘semi-dark’. For the resulting recombination line of such semi-dark complexes, we find that it is shifted downwards in energy (relative to the bright trion line) by 2ΔSO, twice the c-band spin-orbit splitting.

View Article: PubMed Central - PubMed

ABSTRACT

The direct band gap character and large spin-orbit splitting of the valence band edges (at the K and K’ valleys) in monolayer transition metal dichalcogenides have put these two-dimensional materials under the spot-light of intense experimental and theoretical studies. In particular, for Tungsten dichalcogenides it has been found that the sign of spin splitting of conduction band edges makes ground state excitons radiatively inactive (dark) due to spin and momentum mismatch between the constituent electron and hole. One might similarly assume that the ground states of charged excitons and biexcitons in these monolayers are also dark. Here, we show that the intervalley (K ⇆ K′) electron-electron scattering mixes bright and dark states of these complexes, and estimate the radiative lifetimes in the ground states of these “semi-dark” trions and biexcitons to be ~10 ps, and analyse how these complexes appear in the temperature-dependent photoluminescence spectra of WS2 and WSe2 monolayers.

No MeSH data available.