Evidence for moiré excitons in van der Waals heterostructures

Abstract

Recent advances in the isolation and stacking of monolayers of van der Waals materials have provided approaches for the preparation of quantum materials in the ultimate two-dimensional limit^1,2. In van der Waals heterostructures formed by stacking two monolayer semiconductors, lattice mismatch or rotational misalignment introduces an in-plane moiré superlattice³. It is widely recognized that the moiré superlattice can modulate the electronic band structure of the material and lead to transport properties such as unconventional superconductivity⁴ and insulating behaviour driven by correlations^5-7; however, the influence of the moiré superlattice on optical properties has not been investigated experimentally. Here we report the observation of multiple interlayer exciton resonances with either positive or negative circularly polarized emission in a molybdenum diselenide/tungsten diselenide (MoSe₂/WSe₂) heterobilayer with a small twist angle. We attribute these resonances to excitonic ground and excited states confined within the moiré potential. This interpretation is supported by recombination dynamics and by the dependence of these interlayer exciton resonances on twist angle and temperature. These results suggest the feasibility of engineering artificial excitonic crystals using van der Waals heterostructures for nanophotonics and quantum information applications.

Extended Data Fig. 1 |. Band structure DFT calculation for different stacking types.

a, The three stacking types (${\text{R}}_{\text{h}}^{\text{h}},{\text{R}}_{\text{h}}^{\text{X}}$ and ${\text{R}}_{\text{h}}^{\text{M}}$) of the bilayer MoSe₂/WSe₂ heterostructure and corresponding DFT-calculated band structures. b, Interlayer distance and bandgap of the three stacking types. c, First-principles GW-BSE calculation results for the quasiparticle bandgap and exciton-binding energy of different stacking types.

Extended Data Fig. 2 |. Second-harmonic generation.

a, Polarization-resolved SHG signal as the sample is rotated in a plane normal to the incident laser. The peaks of the SHG signal correspond to the armchair axes of the crystal. b, Schematics of the phase-resolved SHG setup. c, SHG phase-resolved spectra between the monolayers and the beta barium borate crystal with signals in phase for a twist angle of approximately 0° between the monolayers. d, As in c but with out-of-phase signals for a twist angle of approximately 60°.

Extended Data Fig. 3 |. Moiré exciton theory model.

a, Moiré reciprocal lattice vectors in the first shell. b, Real-space map of the centre-of-mass wavefunctions for peak 4. c, d, The spatial variation of the ${\text{σ}}^{+}$ (c) and ${\text{σ}}^{-}$ (d) components of the optical matrix elements.

Extended Data Fig. 4 |. Thermal decay and recombination dynamics of a heterobilayer with a twist angle of 1°.

a, Temperature dependence of the photoluminescence between 25 K and 70 K. b, Time-resolved photoluminescence dynamics (points) at energies close to the four interlayer exciton transitions labelled in the inset. The solid lines are biexponential fits to the data. The inset shows the emission energy dependence of the fast and slow decay times.

Extended Data Fig. 5 |. Comparison of photoluminescence between two heterobilayers with slightly different twist angles.

a, Steady-state photoluminescence spectra from the 1° sample (sample 1) and the 2° sample (sample 2). b, Time-resolved photoluminescence dynamics for interlayer exciton emission at 1,320 meV, as indicated by the shaded area in a.

Extended Data Fig. 6 |. Spectra from different heterobilayer stacking configurations.

Comparison between interlayer exciton resonances from an H-type sample (upper panel) and an R-type sample (lower panel).

Fig. 1 |. Moiré superlattice modulates the electronic and optical properties.

a, Different local atomic alignments occur in a MoSe₂/WSe₂ vertical heterostructure with a small twist angle. The three highlighted regions correspond to local atomic configurations with three-fold rotational symmetry. b, In the K valley, $S_z=0$ interlayer exciton transitions occur between spin-up conduction-band electrons in the MoSe₂ layer and spin-up valence-band electrons in the WSe₂ layer. K-valley excitons obey different optical selection rules depending on the atomic configuration ${\text{R}}_{\text{h}}^{\mu }$ within the moiré pattern. ${\text{R}}_{\text{h}}^{\mu }$ refers to R-type stacking with the $\mu$ site of theMoSe₂ layer aligning with the hexagon centre (h) of the WSe₂ layer. Exciton emission at ${\text{R}}_{\text{h}}^{\text{h}}\left({\text{R}}_{\text{h}}^{\text{X}}\right)$ is left-circularly (right-circularly) polarized. Emission from the ${\text{R}}_{\text{h}}^{\text{M}}$ site is dipole-forbidden for normal incidence. c, Left, the moiré potential of the interlayer exciton transition, showing a local minimum at the ${\text{R}}_{\text{h}}^{\text{h}}$ site. Right, spatial map of the optical selection rules for K-valley excitons. The high-symmetry points are circularly polarized and the regions in between are elliptically polarized.

Fig. 2 |. Photoluminescence from MoSe₂/WSe₂ heterobilayer with 1° twist angle.

a, Optical image of a hBN-encapsulated MoSe₂/WSe₂ stacked heterostructure. The heterobilayer region is indicated inside the black dotted line. b, Comparison of the photoluminescence spectrum from an uncapped heterostructure (dashed black curve) and a hBN-encapsulated heterostructure (solid blue curve). Neutral (X⁰) and charged (X⁻) exciton emission is observed from the MoSe₂ and WSe₂ monolayers. The interlayer exciton emission is observed approximately 300 meV below the intralayer resonances. c, Illustrative band diagram showing the type-II alignment and the interlayer exciton transition. a.u., arbitrary units.

Fig. 3 |. Twist-angle dependence and circularly polarized emission.

a, Representative photoluminescence spectra shown for heterobilayers with twist angles of 1° (bottom) and 2° (top). Each spectrum is fitted with four (1°) or five (2°) Gaussian functions. b, The centre energy of each peak obtained from the fits at different spatial positions across each sample. The average peak spacing increases from 22 ± 2 meV to 27 ± 3 meV as the twist angle increases from 1° to 2°. c, Circularly polarized photoluminescence spectrum for σ⁺ excitation of the 1° sample. d, The degree of circular polarization plotted against the emission wavelength obtained from the spectra in c.

Fig. 4 |. Calculated multiple interlayer exciton resonances confined in a moiré supercell.

a, Illustration of the spatial variation of the moiré potential and the confined multiple interlayer exciton resonances. b, Optical conductivity of interlayer excitons in the K valley in response to ${\text{σ}}^{+}$ (blue line) and ${\text{σ}}^{-}$ (red line) polarized light. c–e, Real-space map of the centre-of-mass wavefunctions for peaks 1, 2 and 3, respectively.