Abstract
Interlayer excitons (ILXs) — electron–hole pairs bound across two atomically thin layered semiconductors — have emerged as attractive platforms to study exciton condensation1,2,3,4, single-photon emission and other quantum information applications5,6,7. Yet, despite extensive optical spectroscopic investigations8,9,10,11,12, critical information about their size, valley configuration and the influence of the moiré potential remains unknown. Here, in a WSe2/MoS2 heterostructure, we captured images of the time-resolved and momentum-resolved distribution of both of the particles that bind to form the ILX: the electron and the hole. We thereby obtain a direct measurement of both the ILX diameter of around 5.2 nm, comparable with the moiré-unit-cell length of 6.1 nm, and the localization of its centre of mass. Surprisingly, this large ILX is found pinned to a region of only 1.8 nm diameter within the moiré cell, smaller than the size of the exciton itself. This high degree of localization of the ILX is backed by Bethe–Salpeter equation calculations and demonstrates that the ILX can be localized within small moiré unit cells. Unlike large moiré cells, these are uniform over large regions, allowing the formation of extended arrays of localized excitations for quantum technology.
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Acknowledgements
We acknowledge support for optical spectroscopy measurements, data analysis, sample characterization, and sample fabrication from the AMOS program, Chemical Sciences, Geosciences, and Biosciences Division, Basic Energy Sciences, U.S. Department of Energy. Sample preparation was also supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant number GBMF9462 and made use of the facilities in the Stanford Nano Shared Facilities (SNSF), supported by the National Science Foundation under award ECCS-1542152. We thank the OIST engineering support section and Y. Yamauchi from the OIST Facilities Operations and Use section for their support. The TR-µ-ARPES instrumentation, data acquisition and preliminary analysis were supported by the Femtosecond Spectroscopy Unit, Kick-start fund KICKS. XUV generation technology was supported by OIST Innovative Technology – Proof of Concept Program at the Okinawa Institute of Science and Technology Graduate University. The computational work was supported by the Center for Computational Study of Excited-State Phenomena in Energy Materials, which is funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under contract no. DE-AC02-05CH11231, as part of the Computational Materials Sciences Program. We acknowledge the use of computational resources at the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the US DOE under the above contract. Funding: AMOS program, Chemical Sciences, Geosciences, and Biosciences Division, Basic Energy Sciences, U.S. Department of Energy (T.F.H., O.K., E.B., H.B.R.). Gordon and Betty Moore Foundation’s EPiQS Initiative through grant number GBMF9462 (J.H., A.L.O.). Koret Foundation (O.K.). Natural Science and Engineering Research Council (NSERC) of Canada, fellowship PGSD3-502559-2017 (E.B.). NTT Research Fellowship (J.H.). Femtosecond Spectroscopy Unit – Okinawa Institute of Science and Technology Graduate University (V.P., M.K.L.M., C.S., D.R.B., X.Z., A.A.-M., M.M.M.A., N.S.C., A.K., A.J.W., J.M., K.M.D.). Okinawa Institute of Science and Technology Graduate University Innovative Technology Research – Proof of Concept Program (K.M.D.). JSPS KAKENHI grant no. JP17K04995 (M.K.L.M.). Kick-start fund KICKS – Okinawa Institute of Science and Technology Graduate University (K.M.D., N.S.C.). JSPS KAKENHI grant no. 21H01020 (J.M.). FAPESP for post-doctoral fellowships, grant nos. 2018/04926-9 and 2017/20100-00 (H.B.R.). National Science Foundation Materials Research Science and Engineering Centers DMR-1420634 and DMR-2011738 (K.B., B.K.). Elemental Strategy Initiative, conducted by the MEXT, Japan, grant no. JPMXP0112101001 (K.W., T.T.). JSPS KAKENHI grant nos. 19H05790 and JP20H00354 (K.W., T.T.). Department of Energy Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under contract no. DE-AC02-05CH11231 (F.H.dJ., J.D.G.).
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O.K., E.B. and K.M.D. conceived the project. K.W., T.T., B.K. and K.B. supplied raw materials for sample fabrication. E.B. and O.K., supported by A.L.O., H.B.R. and J.H. fabricated the samples. V.P., M.K.L.M. and C.S. collected the data, with assistance from D.R.B., X.Z., A.A.-M., M.M.M.A., A.K., A.J.W. and J.M. V.P., M.K.L.M., C.S., N.S.C. and X.Z. performed preliminary analysis. E.B. and O.K. analysed the data. F.H.dJ. and J.D.G. performed theoretical calculations. J.D.G. was supervised by F.H.dJ. A.L.O., E.B., H.B.R., J.H. and O.K. were supervised by T.F.H. K.M.D. supervised the project. All authors contributed to discussions and manuscript preparations.
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J.M., M.K.L.M. and K.M.D. are inventors on a patent application related to this work filed by the Okinawa Institute of Science and Technology School Corporation (US 2020/0333559 A1 published on October 22, 2020). The authors declare no other competing interests.
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Extended data figures and tables
Extended Data Fig. 1 Reflection contrast spectra of the sample.
Top, reflection of the 1L WSe2 region, showing its lowest excitonic resonance at 1.7 eV, marked with a grey dashed line. Middle, the same, for 1L MoS2, with its lowest resonance at 1.95 eV. Bottom, the same, for the heterobilayer region. It shows several resonances, marked I, II and III, instead of a single line in the vicinity of the WSe2 resonance. This signature has been categorized as evidence for the emergence of the moiré pattern16. All measurements were done at 80 K.
Extended Data Fig. 2 Distortion correction procedures in the momentum microscope.
a, Schematic of the imaging optics in the momentum microscope. To correct for the distortions in the imaging optics, a physical grid was inserted at the back focal plane of the objective lens. b, A cut in the kx–ky plane in the presence of the grid as imaged by the detector before correction. Overlaid on top is a yellow box representing a perfect square. It can be seen that the pattern of the grid is not perfectly square. A weak pincushion distortion is also visible. c, The same, after correction, showing the grid lines conforming to the yellow square. d, A 2D projection of the grid at different electron kinetic energies Ekin, before corrections. The variation of the distortion and magnification with different Ekin is obvious. e, The same, after energy-dependent grid distortion corrections.
Extended Data Fig. 3 Static ARPES data with VB assignment near the K points.
A rescaled version of Fig. 2a, highlighting the MoS2 VBs around the K valleys.
Extended Data Fig. 4 Extracting the exciton-bound electron dispersion.
a, kx ARPES cut of the photoexcited electron signal around the K point. The dashed yellow line is the VB dispersion. b, Selected spectra (EDC) along the dashed orange, green and red lines marked in a, together with the Gaussian fits, demonstrating the negative dispersion of the signal.
Extended Data Fig. 5 TR-μ-ARPES data with above bandgap photoexcitation.
a, A momentum slice along the Γ–K axis of the BZ at t = 0 ps. The photoexcited electrons are scattered over a wide momentum and the shaded energy range above the dashed orange line, with a clear CB dispersion around the K point (yellow dashed indicator). b, Normalized EDC at the K point. The green plot is the equilibrium data. The black plot refers to the data at t = 0 ps. c, The same as a, at t = 50 ps. The photoexcited electrons are concentrated at 1 eV energy (magenta dashed line) with an anomalous dispersion curvature. d, The same as b, for t = 50 ps. The red plot refers to the data at 50-ps delay. This highlights the spectral differences between the unbound (at t = 0 ps) and exciton-bound (at later times) electrons showing up at different energies. The dashed magenta lines at energies below 0 eV indicate the band-edge energies for each VB. In comparison with the equilibrium VB EDC, at t = 50 ps, a reduction in counts is clearly registered for VB 1, associated with WSe2, whereas none is registered for the other VBs, deducing that no holes are accumulating in MoS2. e, Average momentum deviation from the VBM, (kx, ky) = (0, 0) Å−1, of the ILX-bound hole distributions, determined at various time delays using the Gaussian fit. The distribution are clustered on average around (kx, ky) = (0.002, 0.0088) ± (0.0056, 0.0042) Å−1, effectively (within a single-pixel error) at the VBM. f, The same for the ILX-bound electrons. Their distributions are broadly clustered around (kx, ky) = (−0.0139, 0.0381) ± (0.0019, 0.0035) Å−1, deviating from the hole momentum. This is attributed to the expected momentum mismatch between the ILX-bound electrons and holes of a moiré exciton.
Extended Data Fig. 6 Extracting the photoexcited hole distribution.
a, APRES energy–momentum cut along the K–Γ direction around a specific K point for unexcited conditions. b, Fitting the VB with three Gaussians in energy near the centre of the plot in a. c, The same as a, after the photoexcitation. d, The same as b, after the photoexcitation. e, Heat map of the photoemitted counts associated with the top VB of the unperturbed sample. f, The same, after the excitation. Red squares mark the region around [kx0, ky0] used to normalize the counts from each measurement. g, The hole occupation distribution map resulting from the comparison between panels e and f.
Extended Data Fig. 7 Temperature dependence of ILX density and momentum distribution widths at 50-ps delay.
a, ILX density, acquired for two excitation powers, at 100 K and 300 K. The reduction of ILX density with temperature is in line with the expected shortening of their lifetime at elevated temperatures. b, Fitted Gaussian widths of the ILX-bound hole and electron distributions at 100 K and 300 K. The width of the ILX-bound hole distribution hardly changes, whereas the electron distribution shows some broadening within our experimental accuracy. This is consistent with the analysis in the Supplementary Material that predicts little temperature dependence for the widths of Ie(k) and Ih(k). Both excitation powers show very similar distribution widths, ruling out low signal-to-noise ratio issues or many-body effects. The latter is also consistent with the ILX densities being lower than their broadening onset described in Fig. 3e.
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Karni, O., Barré, E., Pareek, V. et al. Structure of the moiré exciton captured by imaging its electron and hole. Nature 603, 247–252 (2022). https://doi.org/10.1038/s41586-021-04360-y
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DOI: https://doi.org/10.1038/s41586-021-04360-y
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