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Tailoring excitonic states of van der Waals bilayers through stacking configuration, band alignment, and valley spin

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Science Advances  20 Dec 2019:
Vol. 5, no. 12, eaax7407
DOI: 10.1126/sciadv.aax7407
  • Fig. 1 Interlayer hybridization of valence bands at K valleys for commensurate TMD heterobilayer.

    (A) Schematic showing the hybridization of electronic states from upper (∣ψu⟩) and lower (∣ψl⟩) layers. (B and C) High-symmetry R-type (B) and H-type (C) stacking configurations, where the top (side) view is shown in the upper (lower) panel. Rνμ (Hνμ) denotes an R-type (H-type) stacking with μ sites of the upper layer vertically aligned with ν sites of the lower layer, where μ, ν = M or X. (D and E) The interlayer hopping integral ∣tvv∣ as a function of interlayer translation r for R-type (D) and H-type (E) heterobilayers, where the dots correspond to the high-symmetry stacking configurations shown in (B) and (C), respectively. (F) ∣tvv∣ of R-type (blue) and H-type (red) heterobilayers along the dashed diagonal line are shown for comparison.

  • Fig. 2 Layer-hybridized valley excitons in the WSe2/MoSe2 heterobilayer.

    (A and B) TEM and Bragg-filtered (inset) images of RMX (A) and HXM (B) heterobilayers. The ideal atomic registry is illustrated for comparison, where the top (side) view is shown in the upper (lower) panel. Scale bars, 1 nm. (C) The differential reflectance (DR; upper panel) and second derivative (lower panel) spectra of an RMX (blue curves) and an HXM (red curves) heterobilayer, showing a clear splitting of XBW for the HXM heterobilayer. (D) The DR (upper panel) and second derivative (lower panel) spectra of an HXM heterobilayer shown with the spectra fitting (red curve). (E) Schematic showing the optical transitions of the HXM heterobilayer at K valley. Note that both XBW (blue) and XAMo (orange) transitions are split into two hybridized transitions (Xh±W and Xh±Mo), corresponding to the fitting curves in (D). The transitions form Λ-shape level schemes that allow the interlayer quantum control of electrons. (F) Schematics showing the wave functions in the out-of-plane direction for the four species of layer-hybridized valley excitons, featuring both large optical dipoles and large electric dipoles compared with that of monolayer and interlayer excitons. (G) A schematic showing the spin valley–selective interlayer quantum control of electron states by Xh±W and Xh±Mo transitions intermediated via an interlayer negative trion IX. a.u., arbitrary units.

  • Fig. 3 Layer-hybridized valley excitons in the WS2/MoS2 heterobilayer.

    (A to C) TEM and Bragg-filtered (inset) images of RMX (A), RXM (B), and HXM (C) heterobilayers. The ideal atomic registry is illustrated for comparison, where the top (side) view is shown in the upper (lower) panel. Scale bars, 0.5 nm. (D) The second derivative spectra as a function of twist angle θ. Only the HXM heterobilayer exhibits interlayer hybridization. (E) A comparison of RMX and HXM heterobilayers (upper panel), showing a clear splitting of XBW for the HXM heterobilayer. The second derivative spectrum (lower panel) of the HXM heterobilayer with spectral fitting (red curve).

  • Fig. 4 Partially layer-hybridized valley excitons in bilayer MoS2.

    (A) The second derivative spectra of bilayer MoS2 as a function of twist angle θ. (B) The energy separation between XAMo and XBMo as a function of θ, where the HXM bilayer is a singular point featuring a separation larger by ~20 meV. (C) Schematic showing the optical transitions of spin-up excitons in the HXM heterobilayer at K valleys, where both XAMo and XBMo transitions are split into hybridized transitions (Xh+o,e and Xho,e). Note that the valence band spin splitting in the HXM bilayer is increased from 2λ to 2λ2+t2 by the presence of finite interlayer hopping (t), whereas in the RMX bilayer, the interlayer hybridization is absent by symmetry. (D and E) Schematics showing the wave functions in the out-of-plane direction for the eight species of partially layer-hybridized excitons per valley with spin up (D) and spin down (E). Note four of them Xho have large optical dipoles (moderate electric dipoles) of ~97% (~25%) compared with that of monolayer (interlayer) exciton. The other four Xhe have large electric dipoles (moderate optical dipoles) of ~97% (~25%) compared with that of interlayer (monolayer) exciton.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/12/eaax7407/DC1

    Fig. S1. Room temperature characterizations of WSe2/MoSe2 heterobilayers by Raman and PL spectroscopies.

    Fig. S2. Room temperature characterizations of WS2/MoS2 heterobilayers by Raman and PL spectroscopies.

    Fig. S3. Room temperature characterizations of MoS2 homobilayers by Raman and PL spectroscopies.

    Fig. S4. Strain effect of commensurate WSe2/MoSe2 heterobilayers.

    Fig. S5. Optical transitions of HXM WSe2/MoSe2 heterobilayer.

    Fig. S6. Temperature-dependent DR spectra of HXM WSe2/MoSe2 heterobilayer.

    Fig. S7. TEM characterizations of bilayer MoS2.

    Fig. S8. Low-temperature PL of WSe2/MoSe2 heterobilayer with R-type and H-type stackings.

    Fig. S9. Scanning TEM images at different locations of WSe2/MoSe2 heterobilayer with R-type and H-type stackings.

    Fig. S10. DR spectrum of WS2/MoS2 heterobilayer with H-type stacking.

    Note S1. Low-temperature PL measurements.

    References (3033)

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Room temperature characterizations of WSe2/MoSe2 heterobilayers by Raman and PL spectroscopies.
    • Fig. S2. Room temperature characterizations of WS2/MoS2 heterobilayers by Raman and PL spectroscopies.
    • Fig. S3. Room temperature characterizations of MoS2 homobilayers by Raman and PL spectroscopies.
    • Fig. S4. Strain effect of commensurate WSe2/MoSe2 heterobilayers.
    • Fig. S5. Optical transitions of HXM WSe2/MoSe2 heterobilayer.
    • Fig. S6. Temperature-dependent DR spectra of HXM WSe2/MoSe2 heterobilayer.
    • Fig. S7. TEM characterizations of bilayer MoS2.
    • Fig. S8. Low-temperature PL of WSe2/MoSe2 heterobilayer with R-type and H-type stackings.
    • Fig. S9. Scanning TEM images at different locations of WSe2/MoSe2 heterobilayer with R-type and H-type stackings.
    • Fig. S10. DR spectrum of WS2/MoS2 heterobilayer with H-type stacking.
    • Note S1. Low-temperature PL measurements.
    • References (3033)

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