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Ultrafast nano-imaging of dark excitons

Nature Photonics volume 19, pages 187–194 (2025)Cite this article

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Abstract

Understanding the impact of spatial heterogeneity on the behaviour of two-dimensional materials represents one of the grand challenges in applying these materials in optoelectronics and quantum information science. For transition metal dichalcogenide heterostructures in particular, direct access to heterogeneities in the dark-exciton landscape with nanometre spatial and ultrafast time resolution is highly desired but remains largely elusive. Here we report how ultrafast dark-field momentum microscopy can spatio-temporally resolve dark-exciton formation dynamics in a twisted WSe2/MoS2 heterostructure with a time resolution of 55 fs and a spatial resolution of 480 nm. This enables us to directly map spatial heterogeneity in the electronic and excitonic structure, and to correlate this with the dark-exciton formation and relaxation dynamics. The advantage of the simultaneous ultrafast nanoscale dark-field momentum microscopy and spectroscopy reported here is that it enables spatio-temporal imaging of the photoemission spectral function that carries energy- and momentum-resolved information on the single-particle band structure, many-body interactions and correlation phenomena.

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Fig. 1: Real- and momentum-space characterization of the WSe2/MoS2 heterostructure and working principle of the ultrafast dark-field momentum microscope.
Fig. 2: Spatio-temporal snapshots of the formation and relaxation dynamics of intralayer K excitons and momentum-indirect ILXs.
Fig. 3: Spatio-spectral imaging of the energy landscape of bright K excitons and dark ILXs.
Fig. 4: Correlation of ILX formation dynamics and energy landscape of excitons.

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All of the data needed to evaluate the conclusions are provided within the article and its Extended Data.

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Acknowledgements

This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 217133147/SFB 1073, projects B07 and B10, 432680300/SFB 1456, project B01 and 223848855/SFB 1083, project B9, as well as regular DFG project 512604469. A.A. and S.H. acknowledge funding from EPSRC (EP/T001038/1, EP/P005152/1). A.A. acknowledges financial support by the Saudi Arabian Ministry of Higher Education. K.W. and T.T. acknowledge support from the JSPS KAKENHI (grant numbers 20H00354, 21H05233 and 23H02052) and World Premier International Research Center Initiative (WPI), MEXT, Japan.

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Authors and Affiliations

  1. I. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany

    David Schmitt, Jan Philipp Bange, Wiebke Bennecke, Marco Merboldt, Jonas Pöhls, Sabine Steil, Daniel Steil, R. Thomas Weitz, G. S. Matthijs Jansen, Stefan Mathias & Marcel Reutzel

  2. Fachbereich Physik, Philipps-Universität, Marburg, Germany

    Giuseppe Meneghini, Samuel Brem & Ermin Malic

  3. Department of Engineering, University of Cambridge, Cambridge, UK

    AbdulAziz AlMutairi & Stephan Hofmann

  4. Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe

  5. Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

    Takashi Taniguchi

  6. International Center for Advanced Studies of Energy Conversion (ICASEC), University of Göttingen, Göttingen, Germany

    R. Thomas Weitz & Stefan Mathias

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  1. David Schmitt
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Contributions

S.S., D. Steil, R.T.W., S.H., S.B., G.S.M.J., E.M., S.M. and M.R. conceived the research. D. Schmitt, J.P.B., W.B. and M.M. carried out the time-resolved momentum microscopy experiments. D. Schmitt and J.P.B. analysed the data. G.M. performed the microscopic model calculations. A.A. fabricated the samples. J.P. and D. Schmitt performed the AFM and KPFM measurements. All authors discussed the results. S.M. and M.R. were responsible for the overall project direction and wrote the paper with contributions from all co-authors. K.W. and T.T. synthesized the hBN crystals.

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Correspondence to Stefan Mathias or Marcel Reutzel.

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Nature Photonics thanks Dmytro Kutnyakhov, Simone Latini and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Determination of the twist angle of the WSe2/MoS2 heterostructure and characterization of the ILX formation mechanism.

a,b Momentum fingerprints of the WSe2 K-exciton a and the MoS2 K-exciton b after photoexcitation with 1.7 eV and 1.9 eV, respectively (pump-probe delay of 40 fs). The Brillouin zones of WSe2 (orange) and MoS2 (dark red, dashed) are overlaid onto the data as hexagons. The twist angle θ can be directly determined from the misalignment of the WSe2 and MoS2 K valleys (labelled as KW and KMo). c Pump-probe delay evolution of energy-distribution curves (EDCs) extracted on the momenta of the optically-excited K-exciton (left panel), the hybrid hΣ-exciton (middle panel) and the ILX (right panel). d By integrating the spectral weight in the energy-windows indicated by the colored rectangles in c, the delay-dependent photoemission signal can be directly compared. A temporal hierarchy of photoemission yield from K-excitons (orange), hΣ-excitons (grey) and ILX (black) is observed. Note, that panel c shows unnormalized EDCs and d normalized delay-dependent photoemission signals.

Extended Data Fig. 2 AFM, KPFM image of the moiré heterostructure and real-space resolved photoemission maps of the pump and the probe laser pulses.

a,b The WSe2 and MoS2 monolayers and the WSe2/MoS2 heterostructure are indicated by orange, dark-red (dashed) and black polygons, respectively. In addition, the bulk TMD and the hBN regions are labelled. a AFM image of the heterostructure. The inset shows two line profiles taken across a blister (blue line) and across a smooth sample area (green line) of the heterostructure. b KPFM image of the heterostructure. We extract the difference in the surface potential on WSe2/hBN (green ROI), on the left-hand side of the WSe2/MoS2/hBN structure (purple ROI) and on the right-hand side of the WSe2/MoS2/hBN structure (red ROI) to ΔV0 = 0.20 V, ΔV1 = 0.24 V and ΔV2 = 0.25 V, respectively. c,d Real-space resolved photoemission maps of the pump (c) and the probe (d) laser pulses. Within the dimension of the heterostructure, indicated with a black polygon in the inset, a homogeneous excitation profile (c) and a homogeneous photoemission efficiency (d) can be expected. The scale bars in a, b, c and d apply to the horizontal and vertical directions.

Extended Data Fig. 3 Correction of space-charge and surface photovoltage effects.

a The time-of-flight (TOF) energy of the peak position indicated in the inset of b is shown as a function of total measurement time for nine measurement delay-cycles (indicated by dashed vertical lines, dark-field aperture positioned on the ILX signal). Without the correction of the spatially averaged rigid energy shift, in each measurement cycle, we find similar dynamics induced by space-charge and surface photovoltage effects. b After the subtraction of the rigid band shift, the spatially averaged TOF energy is constant over the entire measurement time. c,d Selected energy-distribution curves taken at -915 fs and 435 fs in the measurement cycle (labelled as colored vertical lines in panels a and b). The visual comparison of the energy-distribution-curve c before and d after the correction shows that the rigid shift is properly corrected. e Energy map reproduced from Fig. 3c of the main text (dark-field aperture positioned on the K-exciton signal). The heat-map encodes the peak position of the top WSe2 valence band. f EDCs taken at pump-probe delays of -936 fs (before optical excitation) and 34 fs (after pump-probe overlap) in the regions-of-interest that are color-coded by the squares in e. The solid vertical line indicates the center position of peak (III). Peaks (I) and (II) are the spin-split valence bands of WSe2. The center positions of all peaks are evaluated by applying Gaussians fits. g Pump-probe delay evaluation of the extracted peak positions of the top WSe2 valence bands in the two-regions of interest indicated in e. The respective errors are extracted from the Gaussian fitting procedure. h Real-space photoemission map in an energy region between -0.36 and 0.24 eV (colored region in j) with the dark-field aperture positioned at the KW-valley. i AFM image of the same sample region. j EDCs extracted from the circular ring apertures shown in h and i. The scale bars in e, h and i apply to the horizontal and vertical directions.

Extended Data Fig. 4 Image correction in dark-field momentum microscopy.

a The WSe2 (orange) and MoS2 (dark red, dashed) monolayers and the WSe2/MoS2-heterostructure (black) and blisters (blue points) can be identified in the 30 μm × 30 μm AFM image. b Exemplary real-space image of the full field-of-view measured with the momentum microscope at an energy of E-EV BM,avg = -0.5 eV. The dark-field aperture is positioned at the in-plane momenta of the ILX. The boundaries of the WSe2 and MoS2 monolayers as well as the blister positions are indicated. c Based on an affine transformation, the AFM and photoemission images are aligned. d Distortion field of the applied transformation. The scale bars in a, b and c apply to the horizontal and vertical directions.

Extended Data Fig. 5 Additional spatio-temporal snapshots and comparison to the momentum-resolved experiment.

a, b Real-space snapshots of the formation and relaxation dynamics of bright K-excitons (a) and ILXs (b). c Pump-probe delay-dependent analysis of the photoemission yield of the K-exciton and the ILX in the WSe2/MoS2 heterobilayer (orange and black) and the WSe2 monolayer (brown). The data points are obtained in the dark-field momentum microscopy experiment by integrating photoelectron counts inside the heterobilayer and monolayer regions. The grey data points are generated from a spatially-averaged trARPES experiment with an aperture positioned in the real-space plane of the microscope (cf. blue circle in Fig. 1a). The scale bars in a and b apply to the horizontal and vertical directions.

Extended Data Fig. 6 Calibration of the energy- and the pump-probe-delay axis in the dark-field momentum microscopy experiment.

a In-plane momentum-resolved photoemission data taken at a pump-probe delay of 10 ps and the energy centered on the WSe2 VBM. The blue, cyan and red circle indicate different aperture sizes used to create the EDCs in b. The size of the dark-field aperture corresponds to the blue circle. b EDCs obtained by integrating the photoemission yield in the respective momentum-regions of interest indicated in a. In all EDCs, the energetically highest photoemission peak is attributed to the WSe2 VBM. With increasing diameter of the aperture in momentum space, the peak maxima shift to smaller energies. A quantitative analysis shows an energetic offset of 0.23 eV between the 1 × aperture (that is, the size of the dark-field aperture) and 0.21 × aperture. The peak position of the 0.21 × aperture is set as reference point and the spatial-resolved data is calibrated with respect to the extracted offset-value. c Pump-probe delay-dependent analysis of the photoemission intensity of K-excitons and ILXs as extracted in the dark-field experiment (orange and black) and the spatially averaged trARPES experiment (grey).

Extended Data Fig. 7 Real-space resolved heatmaps of the formation time, the energy landscape and the respective errors.

a ILX formation map and respective absolute errors. b-e Spatio-spectral heatmaps (top row) and respective absolute error maps (bottom row). The scale bars in all images apply to the horizontal and vertical directions.

Extended Data Fig. 8 Benchmarking of the real-space resolution of the dark-field momentum microscopy experiment.

a In the momentum microscopy experiment with the dark-field aperture placed on the in-plane momenta of the ILX at an energy range from -1.69 eV to -1.49 eV (occupied valence bands) and a photon energy of 26.5 eV, the spatial resolution is determined to 472 ± 16 nm. b If the same analysis is done on the excitonic photoemission yield, that is, integrated over all energies above 0.6 eV, a spatial resolution of 481 ± 79 nm is extracted. All green lines in the lower panels are error function fits, from which we extract the FWHM as the spatial resolution. The scale bars in a and b apply to the horizontal and vertical directions.

Extended Data Fig. 9 Overview of correlation maps.

From left to right, the ILX formation time is correlated with the WSe2 top valence band energy EVBM, the K-exciton energy \({E}_{{\rm{exc}}}^{{\rm{K}}}\), ILX energy \({E}_{{\rm{exc}}}^{{\rm{ILX}}}\) and the exciton energy difference Δ\({E}_{\exp }^{{\rm{K}},{\rm{ILX}}}\). The color scale represents the normalized point density.

Extended Data Fig. 10 Energy landscape of excitons.

Calculated energy landscape of excitons for ΔEsp = 0 eV. The colors represent the contribution of the intralayer tungsten (W, orange), the intralayer molybdenum (Mo, red) and the interlayer (W-Mo, black) exciton character.

Supplementary information

Supplementary Video 1

Time- and real-space-resolved movie of the dark-field filtered photoemission yield from the K excitons.

Supplementary Video 2

Time- and real-space-resolved movie of the dark-field filtered photoemission yield from the ILX.

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Schmitt, D., Bange, J.P., Bennecke, W. et al. Ultrafast nano-imaging of dark excitons. Nat. Photon. 19, 187–194 (2025). https://doi.org/10.1038/s41566-024-01568-y

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