Research ArticleMATERIALS SCIENCE

Shedding light on moiré excitons: A first-principles perspective

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Science Advances  16 Oct 2020:
Vol. 6, no. 42, eabc5638
DOI: 10.1126/sciadv.abc5638
  • Fig. 1 Moiré patterns in the MoS2/WS2 heterobilayer.

    The unit cell of the moiré superlattice formed by a twisted MoS2/WS2 heterostructure with angle θ = 3.48° (A) and θ = 56.52° (B). The stacking configurations of the three local motifs, A, B, and C, are shown on the right.

  • Fig. 2 Moiré-modulated local energy gaps and interlayer distances.

    (A) The definition of in-plane displacement d in the primitive unit cell of the MoS2/WS2 heterostructure with θ = 0° (left). The definition of three bandgaps, Eg, Δ1, and Δ2 (right). (B) Variation of the MoS2/WS2 bandgap (Eg) as a function of d, showing three extremes at the A, B, and C points. (C) Variation of the interlayer distance δh as a function of d, with the extremes at the A, B, and C points.

  • Fig. 3 Flat bands in twisted MoS2/WS2 heterostructures.

    (A) The single-particle band structure for the MoS2/WS2 heterostructure with θ = 56.52°. The CBM and VBM bands are shown in red and blue, respectively. (B) Top and side views of the charge density of the CBM and VBM bands for the heterostructure. The unit cell of the moiré lattice is indicated by the dashed box. (C) Band structure for the MoS2/WS2 heterostructure with θ = 3.48°. (D) Top and side views of the charge density of the CBM and VBM bands for the heterostructure.

  • Fig. 4 Localized moiré excitons in the twisted MoS2/WS2 heterostructure (θ = 3.48°).

    (A) Charge density and energy for the lowest-energy exciton in the MoS2/WS2 heterostructure with θ = 0° (upper panel, top view; bottom panel, side view). (B to D) Charge density and energy for the three lowest-energy moiré excitons in the twisted MoS2/WS2 heterostructure with θ = 3.48° (upper panel, top view; bottom panel, side view). The dashed box indicates the unit cell of the moiré superlattice. Red and blue colors represent the charge density of the electron and the hole, respectively. All iso-surface values are set at 0.0001 e/A3.

  • Fig. 5 Localized moiré excitons in the twisted MoS2/WS2 heterostructure (θ = 56.52°).

    (A to D) Charge density and energy for the four lowest-energy moiré excitons in the twisted MoS2/WS2 heterostructure with θ = 56.52° (upper panel, top view; bottom panel, side view). The dashed box indicates the unit cell of the moiré superlattice. Red and blue colors represent the charge density of the electron and the hole, respectively. All iso-surface values are set at 0.0001 e/Å3.

  • Fig. 6 Electric field tunable electronic structure in the MoS2/WS2 heterostructure.

    (A) Top: Schematic picture of the MoS2/WS2 heterostructure under a perpendicular electric field ε. The dipole moment of the interlayer exciton is indicated by P. Bottom: Electric tuning of the type II band alignment of the heterostructure. The red and blue arrows denote the energy level shift directions. (B) The variation of the interlayer distance h at the A, B, and C points for the MoS2/WS2 heterostructure with θ = 3.48°.

  • Fig. 7 Tuning moiré excitons in the twisted MoS2/WS2 heterostructure by electric field.

    (A to C) The charge density distribution (top and side views) for the lowest-energy moiré exciton in the MoS2/WS2 heterostructure with θ = 3.48° under different electric fields. Red and blue colors represent the charge density of the electron and the hole, respectively. (D) The density of states (DOS) for the excitons under different electric fields, showing field-tunable exciton transition energies. The spatial locations (A, B, and C) for the two lowest-energy excitons are indicated.

  • Fig. 8 Tuning hybridized moiré excitons by electric field.

    (A) The side view of the charge density distribution for the lowest-energy exciton in the MoS2/WS2 heterostructure with θ = 56.5° under different electric fields. Red and blue colors represent the charge density of the electron and the hole, respectively. (B) Side view of the charge density distribution for the two lowest-energy excitons in the MoS2/WS2 heterostructure with θ = 3.48° under the electric field of ε = 3 V/nm.

  • Fig. 9 Tuning moiré exciton diffusion by electric field.

    (A) Schematic diagram showing the dipole directions of a diffusing moiré exciton from the B point to the C point in a moiré superlattice. (B) Schematic picture depicting the fluctuation of the dipole moment of a diffusing moiré exciton under an alternating electric field.

Supplementary Materials

  • Supplementary Materials

    Shedding light on moiré excitons: A first-principles perspective

    Hongli Guo, Xu Zhang, Gang Lu

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