Twist-angle-dependent interlayer exciton diffusion in WS2–WSe2 heterobilayers


The nanoscale periodic potentials introduced by moiré patterns in semiconducting van der Waals heterostructures have emerged as a platform for designing exciton superlattices. However, our understanding of the motion of excitons in moiré potentials is still limited. Here we investigated interlayer exciton dynamics and transport in WS2–WSe2 heterobilayers in time, space and momentum domains using transient absorption microscopy combined with first-principles calculations. We found that the exciton motion is modulated by twist-angle-dependent moiré potentials around 100 meV and deviates from normal diffusion due to the interplay between the moiré potentials and strong exciton–exciton interactions. Our experimental results verified the theoretical prediction of energetically favourable K–Q interlayer excitons and showed exciton-population dynamics that are controlled by the twist-angle-dependent energy difference between the K–Q and K–K excitons. These results form a basis to investigate exciton and spin transport in van der Waals heterostructures, with implications for the design of quantum communication devices.

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Fig. 1: Moiré superlattice and interlayer exciton emission in WS2–WSe2 heterobilayers.
Fig. 2: Moiré potentials in WS2-WSe2 heterobilayers calculated with DFT.
Fig. 3: Interlayer exciton transport modulated by moiré potentials.
Fig. 4: Twist-angle- and temperature-dependent K–K and K–Q interlayer exciton dynamics.

Data availability

The data represented in Figs. 14 and Extended Data Figs. 2–8 are provided with the article as source data. All the other data that support the results in this article are available from the corresponding author upon reasonable request.

Code availability

The codes used for exciton diffusion simulation are available from the corresponding author upon reasonable request.


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The optical spectroscopy and microscopy work at Purdue is supported by the US Department of Energy, Office of Basic Energy Sciences, through award DE-SC0016356. L.Y. also acknowledges support from the Purdue University Bilsland Dissertation Fellowship. L.Y. thanks Y. Wan and Z. Guo for their assistance in the instrument development. B.Z. and A.P. acknowledge the National Natural Science Foundation of China (nos 51525202 and U19A2090). A.B.K., J.K. and T.B. acknowledge ZIH Dresden for computational support. A.B.K. thanks the GRK 2247/1 (QM3) for financial support. J.K. acknowledges funding by the German Research Foundation (DFG) under grant no. SE 651/45-1.

Author information




L.Y. and L.H. designed the experiments, L.Y. carried out the optical measurements, B.Z., A.P. and C.M. grew the samples and performed the electron microscopy characterization, T.B., J.K. and A.B.K. carried out and analysed the DFT calculations, L.Y., L.H., S.D., A.P. and D.B. analysed experimental data and L.Y. and L.H. wrote the manuscript with input from all the authors.

Corresponding author

Correspondence to Libai Huang.

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Extended data

Extended data Fig. 1 Scanning transmission electron microscopy (STEM) images.

a, STEM image of a 0° heterobilayer. The moiré superlattice is marked by white solid lines showing a periodicity of ~ 7.6 nm. b, Schematic of the moiré pattern of the WS2-WSe2 heterobilayers and their supercells (black) for a twist angle of 0°, respectively. Brown, yellow, and orange circles mark regions with high-symmetry stacking configurations. c, Large-scale STEM image for a 60° heterobilayer.

Extended Data Fig. 2 Interlayer exciton transport in a 0° heterobilayer.

The data shown here are from the 0° heterobilayer imaged in Fig. 3b. a, Exciton-density-dependent diffusion for the 0° heterobilayer. b, Temperature-dependent interlayer exciton diffusion for the 0° heterobilayer with an initial exciton density of 4.1 × 1012 cm−2. Solid lines are fits using equation (1). Source data

Extended Data Fig. 3 Exciton-density-dependent PL spectra at 78 K.

a, Intralayer A exciton emission of 1L-WS2. b, Interlayer exciton emission of WS2-WSe2 (60°). Blue shifting of emission energy is observed for the interlayer excitons with increased exciton density in the WS2-WSe2 (60°) due to the net repulsive exciton-exciton interaction. In contrast, such blueshift is not observed in the 1L-WS2. Source data

Extended Data Fig. 4 Exciton-density- and temperature-dependent exciton transport in the WS2 underlayer.

The data shown here are from the WS2 underlayer imaged in Fig. 3b. Intralayer exciton shows a normal diffusion with negligible density dependence and become more mobile at lower temperatures. Solid lines are fits using linear functions. The diffusion constants for 295 and 78 K are fitted to be 0.15 ± 0.04 and 0.44 ± 0.03 cm2 s−1 respectively. The pump and probe photon energies are 3.10 eV and 1.96 eV, respectively. Source data

Extended Data Fig. 5 Exciton-density-dependent interlayer exciton dynamics.

a, the 0° heterobilayer b, the 60° heterobilayer. We ruled out exciton-exciton annihilation effects because exciton dynamics did not show significant density dependence under our experimental conditions. Source data

Extended Data Fig. 6 Interlayer exciton transport in different samples.

a,b, Interlayer exciton transport at different exciton densities at 295 K for 0° and 60°, respectively, in Sample #2. c,d, Interlayer exciton transport at different exciton densities at 295 K for 0° and 60°, respectively, in Sample #3. e,f, Comparing interlayer exciton transport in three 0° heterobilayers and three 60° heterobilayers. Solid lines are simulations using equation (1) described in the main text. The results from sample #1 are also shown in Fig. 3 in the main text and in Extended Data Fig. 2. Source data

Extended Data Fig. 7 Electron dynamics in a total number of 16 heterobilayers at 295 K.

We observed reproducible twist-angle dependent dynamics in different samples. Source data

Extended Data Fig. 8 Temperature-dependent exciton dynamics in the 1L-WS2.

Pump and probe photon energies are 3.1 and 2.0 eV, respectively. Solid lines are fits using a bi-exponential decay function convoluted with a Gaussian function, which gives the decay constants of 122 ± 7 ps at 78 K and 35 ± 1 ps at 295 K. Source data

Supplementary information

Supplementary Information

Supplementary Notes 1–5, Figs. 1–19 and Tables 1–5.

Source data

Source Data Fig. 1

Experimental data points of Fig. 1e,f.

Source Data Fig. 2

Experimental data points of Fig. 2b.

Source Data Fig. 3

Experimental data points of Fig. 3b–f.

Source Data Fig. 4

Experimental data points of Fig. 4b–f.

Source Data Extended Data Fig. 2

Experimental data points of Extended Data Fig. 2a,b.

Source Data Extended Data Fig. 3

Experimental data points of Extended Data Fig. 3a,b.

Source Data Extended Data Fig. 4

Experimental data points of Extended Data Fig. 4.

Source Data Extended Data Fig. 5

Experimental data points of Extended Data Fig. 5a,b.

Source Data Extended Data Fig. 6

Experimental data points of Extended Data Fig. 6a–f.

Source Data Extended Data Fig. 7

Experimental data points of Extended Data Fig. 7.

Source Data Extended Data Fig. 8

Experimental data points of Extended Data Fig. 8.

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Yuan, L., Zheng, B., Kunstmann, J. et al. Twist-angle-dependent interlayer exciton diffusion in WS2–WSe2 heterobilayers. Nat. Mater. 19, 617–623 (2020).

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