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Quadrupolar–dipolar excitonic transition in a tunnel-coupled van der Waals heterotrilayer

Nature Materials volume 22, pages 1478–1484 (2023)Cite this article

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Abstract

Strongly bound excitons determine light–matter interactions in van der Waals heterostructures of two-dimensional semiconductors. Unlike fundamental particles, quasiparticles in condensed matter, such as excitons, can be tailored to alter their interactions and realize emergent quantum phases. Here, using a WS2/WSe2/WS2 heterotrilayer, we create a quantum superposition of oppositely oriented dipolar excitons—a quadrupolar exciton—wherein an electron is layer-hybridized in WS2 layers while the hole localizes in WSe2. In contrast to dipolar excitons, symmetric quadrupolar excitons only redshift in an out-of-plane electric field. At higher densities and a finite electric field, the nonlinear Stark shift of quadrupolar excitons becomes linear, signalling a transition to dipolar excitons resulting from exciton–exciton interactions, while at a vanishing electric field, the reduced exchange interaction suggests antiferroelectric correlations between dipolar excitons. Our results present van der Waals heterotrilayers as a field-tunable platform to engineer light–matter interactions and explore quantum phase transitions between spontaneously ordered many-exciton phases.

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Fig. 1: Quadrupolar and dipolar excitons in a transition metal dichalcogenide heterostructure.
Fig. 2: Electrical field-tunable dipole hybridization in quadrupolar excitons.
Fig. 3: Electrical control of quadrupolar and dipolar exciton lifetimes.
Fig. 4: Density-driven quadrupolar-to-dipolar exciton transition.

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Data availability

Source data are provided with this paper. All other data that support results in this Article are available from the corresponding author upon reasonable request.

Code availability

The code used for the model in Extended Data Fig. 1 is available in Supplementary Code 1.

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Acknowledgements

We thank H. Harutyunyan for help with lifetime measurements and T. Heinz, L. Yu, B. Shklovskii, R. Rapaport and M. Claassen for insightful discussions. This work was supported by the National Science Foundation (NSF) Emerging Frontiers in Research and Innovation programme (grant no. EFMA-1741691 to A.S.), the NSF Division of Materials Research (award no. 1905809 to A.S.) and the State Secretariat for Education, Research and Innovation (SERI)-funded European Research Council Consolidator Grant TuneInt2Quantum (no. 101043957 to A.S.). The computational work was supported by the European Research Council (no. ERC-2015-AdG694097), the Cluster of Excellence ‘Advanced Imaging of Matter’, the collaborative research centre SFB925 and Grupos Consolidados (no. IT1249-19). We acknowledge support by the Max Planck Institute – New York City Center for Non-equilibrium Quantum Phenomena. The Flatiron Institute is a division of the Simons Foundation. J.Z. acknowledges funding received from the European Union Horizon 2020 research and innovation programme under Marie Sklodowska-Curie Grant Agreement 886291 (PeSD-NeSL). Synthesis of WSe2 (S.L. and J.H.) was supported by the NSF Materials Research Science and Engineering Centers programme through the Columbia University Center for Precision-Assembled Quantum Materials (DMR-2011738). K.W. and T.T. acknowledge support from the Japan Society for the Promotion of Science KAKENHI (grant nos 21H05233 and 23H02052) and World Premier International Research Center Initiative, Ministry of Education, Culture, Sports, Science and Technology, Japan.

Author information

Author notes

  1. These authors contributed equally: Weijie Li, Zach Hadjri, Luka M. Devenica, Jin Zhang.

Authors and Affiliations

  1. Department of Physics, Emory University, Atlanta, GA, USA

    Weijie Li, Zach Hadjri, Luka M. Devenica & Ajit Srivastava

  2. Center for Free Electron Laser Science, Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany

    Jin Zhang & Angel Rubio

  3. Department of Mechanical Engineering, Columbia University, New York, NY, USA

    Song Liu & James Hone

  4. Institute of Microelectronics, Chinese Academy of Sciences, Beijing, China

    Song Liu

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

    Kenji Watanabe

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

    Takashi Taniguchi

  7. Center for Computational Quantum Physics, Simons Foundation Flatiron Institute, New York, NY, USA

    Angel Rubio

  8. Nano-BioSpectroscopy Group, Departamento de Fisica de Materiales, Universidad del País Vasco, San Sebastián, Spain

    Angel Rubio

  9. Department of Quantum Matter Physics, University of Geneva, Geneva, Switzerland

    Ajit Srivastava

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Contributions

A.S., W.L., L.M.D. and Z.H. conceived the project. K.W. and T.T. provided the hBN crystals, and S.L. and J.H. provided the WSe2 crystals. W.L., Z.H. and L.M.D. prepared the samples. W.L., Z.H. and L.M.D. carried out the measurements. J.Z. conducted the DFT calculations. A.S. and A.R. supervised the project. All authors were involved in the analysis of the experimental data and contributed extensively.

Corresponding author

Correspondence to Ajit Srivastava.

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Extended data

Extended Data Fig. 1 Model of exciton de-hybridization and antiferroelectric correlations.

a. Eigenvalues of the 4-state system of two excitons as a function of their interparticle distance. b. ‘Phase diagram’ of the exciton system under E-field and varying exciton density. The color scale indicates the probability that the excitons are in an antiferroelectric configuration. c. Same plot as in panel (b), but with the color bar indicating the logarithm of the ratio of probabilities that the system is found in an antiferroelectric configuration versus an ferroelectric configuration. d. Energy of exciton emission at different densities in absence of external electric field. Red points are data and the blue line is the model output. The density of excitons for the data is determined by setting the exciton density at 1 mW of excitation power of 1.696 eV laser to be 1012 cm−2, and the other powers use the same conversion factor. e. Top panel shows extracted trilayer PL peak positions as a function of E-field at different powers. Legend shows excitation powers of 1.696 eV laser in units of mW. Bottom panel shows the modelled trilayer PL peak positions as a function of E-field at different powers. Legend shows densities in units of 1012 cm−2. Both model and data show a faster slope saturation with power.

Source data

Extended Data Fig. 2 Zero electric field states for trilayer excitons.

a. Electric field dependence of trilayer exciton PL emission at 1 mW with fine voltage steps. The PL emission shows an absent red tail around zero field. b. Integrated red tail intensity of the normalized spectra in panel (a) shows a dip near zero field. The excitation is linearly-polarized.

Source data

Supplementary information

Supplementary Information

Supplementary Figs. 1–13 and Notes 1–3.

Supplementary Code 1

Calculations of model in Extended Data Fig. 1.

Source data

Source Data Fig. 1

Optical measurement source data.

Source Data Fig. 2

Optical measurement source data.

Source Data Fig. 3

Optical measurement source data.

Source Data Fig. 4

Optical measurement source data.

Source Data Extended Data Fig. 1

Optical measurement source data.

Source Data Extended Data Fig. 2

Optical measurement source data.

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Li, W., Hadjri, Z., Devenica, L.M. et al. Quadrupolar–dipolar excitonic transition in a tunnel-coupled van der Waals heterotrilayer. Nat. Mater. 22, 1478–1484 (2023). https://doi.org/10.1038/s41563-023-01667-1

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