Science Advances

Supplementary Materials

This PDF file includes:

  • section S1. Modulated electronic and topographic properties in the heterobilayer moiré
  • section S2. Nanopatterned optical properties of the interlayer excitons in the moiré
  • section S3. Complex hopping of the interlayer excitons in the moiré
  • section S4. Exciton bands in superlattice potential: Exact solution and tightbinding model
  • section S5. Exciton-exciton interactions in the superlattices
  • fig. S1. Schematic of how the interlayer translation vector r0(R) (thick green arrows) changes as a function of in-plane position vector R.
  • fig. S2. The modulations of layer separation δd, interlayer bandgap δEg, and intralayer bandgap δEintra for H-type MoS2/WSe2, R-type MoSe2/WSe2, and H-type MoSe2/WSe2 lattice-matched heterobilayers of various interlayer atomic
    registries.
  • fig. S3. The potential profile of the interlayer excitons in the three types of TMD heterobilayers (compare Eq. 1 in the main text).
  • fig. S4. The ab initio results of the optical matrix elements at various interlayer translations r0.
  • fig. S5. The real-space form of an interlayer exciton wave packet X, with width w << b, corresponds to a Q-space distribution covering all the three main light cones (bright spots).
  • fig. S6. Nanopatterned spin optics of moiré excitons in an H-type MoS2/WSe2 moiré pattern.
  • fig. S7. The six reciprocal lattice vectors in the Fourier components of the excitonic potential, and the obtained hopping magnitudes t0,1,2 as functions of the moiré period b or V/ER.
  • table S1. The parameters for fitting the first-principles results (symbols in fig. S2) with eqs. S2 and S3.
  • table S2. The Cˆ3 quantum number of K-point Bloch function ψc or ψ*v for different rotation centers, taken from Liu et al. (29).
  • table S3. The estimated radiative lifetimes for the interlayer exciton wave packets at A or B site in different heterobilayers with b = 15 nm.
  • References (48–56)

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