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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References
He, K. et al. Tightly bound excitons in monolayer WSe2. Phys. Rev. Lett. 113, 026803 (2014).
Mak, K. F. et al. Tightly bound trions in monolayer MoS2. Nat. Mater. 12, 207–211 (2013).
Yong, C.-K. et al. Valley-dependent exciton fine structure and Autler–Townes doublets from Berry phases in monolayer MoSe2. Nat. Mater. 18, 1065–1070 (2019).
Wang, G. et al. Colloquium: excitons in atomically thin transition metal dichalcogenides. Rev. Mod. Phys. 90, 021001 (2018).
Gu, J. et al. Enhanced nonlinear interaction of polaritons via excitonic Rydberg states in monolayer WSe2. Nat. Commun. 12, 2269 (2021).
Zhang, L. et al. Van der waals heterostructure polaritons with moiré-induced nonlinearity. Nature 591, 61–65 (2021).
Tan, L. B. et al. Interacting polaron-polaritons. Phys. Rev. X 10, 021011 (2020).
Slobodkin, Y. et al. Quantum phase transitions of trilayer excitons in atomically thin heterostructures. Phys. Rev. Lett. 125, 255301 (2020).
Sammon, M. & Shklovskii, B. I. Attraction of indirect excitons in van der Waals heterostructures with three semiconducting layers. Phys. Rev. B 99, 165403 (2019).
Astrakharchik, G., Kurbakov, I., Sychev, D., Fedorov, A. & Lozovik, Y. E. Quantum phase transition of a two-dimensional quadrupolar system. Phys. Rev. B 103, L140101 (2021).
Lozovik, Y. E., Berman, O. L. & Willander, M. Superfluidity of indirect excitons and biexcitons in coupled quantum wells and superlattices. J. Phys. Condens. Matter 14, 12457 (2002).
Dagvadorj, G., Kulczykowski, M., Szymańska, M. H. & Matuszewski, M. First-order dissipative phase transition in an exciton-polariton condensate. Phys. Rev. B 104, 165301 (2021).
Rivera, P. et al. Valley-polarized exciton dynamics in a 2D semiconductor heterostructure. Science 351, 688–691 (2016).
Rivera, P. et al. Observation of long-lived interlayer excitons in monolayer MoSe2–WSe2 heterostructures. Nat. Commun. 6, 6242 (2015).
Li, W., Lu, X., Wu, J. & Srivastava, A. Optical control of the valley Zeeman effect through many-exciton interactions. Nat. Nanotechnol. 16, 148–152 (2021).
Kremser, M. et al. Discrete interactions between a few interlayer excitons trapped at a MoSe2–WSe2 heterointerface. npj 2D Mater. Appl. 4, 8 (2020).
Sun, Z. et al. Excitonic transport driven by repulsive dipolar interaction in a van der Waals heterostructure. Nat. Photon. 16, 79–85 (2022).
Fang, H. et al. Strong interlayer coupling in van der Waals heterostructures built from single-layer chalcogenides. Proc. Natl Acad. Sci. USA 111, 6198–6202 (2014).
Wang, Z., Chiu, Y.-H., Honz, K., Mak, K. F. & Shan, J. Electrical tuning of interlayer exciton gases in WSe2 bilayers. Nano Lett. 18, 137–143 (2018).
Ciarrocchi, A. et al. Polarization switching and electrical control of interlayer excitons in two-dimensional van der Waals heterostructures. Nat. Photon. 13, 131–136 (2019).
Baranowski, M. et al. Probing the interlayer exciton physics in a MoS2/MoSe2/MoS2 van der Waals heterostructure. Nano Lett. 17, 6360–6365 (2017).
Alexeev, E. M. et al. Resonantly hybridized excitons in moiré superlattices in van der Waals heterostructures. Nature 567, 81–86 (2019).
Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moiré heterostructure. Nature 580, 472–477 (2020).
Hsu, W.-T. et al. Tailoring excitonic states of van der Waals bilayers through stacking configuration, band alignment, and valley spin. Sci. Adv. 5, eaax7407 (2019).
Xiao, D., Liu, G.-B., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides. Phys. Rev. Lett. 108, 196802 (2012).
Yu, J. et al. Observation of double indirect interlayer exciton in WSe2/WS2 heterostructure. Opt. Express 28, 13260–13268 (2020).
Paradisanos, I. et al. Efficient phonon cascades in WSe2 monolayers. Nat. Commun. 12, 538 (2021).
Jauregui, L. A. et al. Electrical control of interlayer exciton dynamics in atomically thin heterostructures. Science 366, 870–875 (2019).
Li, W., Lu, X., Dubey, S., Devenica, L. & Srivastava, A. Dipolar interactions between localized interlayer excitons in van der Waals heterostructures. Nat. Mater. 19, 624–629 (2020).
Schmitt-Rink, S., Chemla, D. & Miller, D. A. Theory of transient excitonic optical nonlinearities in semiconductor quantum-well structures. Phys. Rev. B 32, 6601–6609 (1985).
Rochat, G. et al. Excitonic Bloch equations for a two-dimensional system of interacting excitons. Phys. Rev. B 61, 13856–13862 (2000).
Schwartz, I. et al. Electrically tunable Feshbach resonances in twisted bilayer semiconductors. Science 374, 336–340 (2021).
Huang, Y. & Shklovskii, B. Biexciton crystal in a pentalayer WSe2/MoSe2/WSe2/MoSe2/WSe2. Preprint at https://doi.org/10.48550/arXiv.2207.11319 (2022).
Zimmerman, M., Rapaport, R. & Gazit, S. Collective interlayer pairing and pair superfluidity in vertically stacked layers of dipolar excitons. Proc. Natl Acad. Sci. USA 119, e2205845119 (2022).
Zhang, Y.-H., Sheng, D. & Vishwanath, A. SU(4) chiral spin liquid, exciton supersolid, and electric detection in moiré bilayers. Phys. Rev. Lett. 127, 247701 (2021).
Zeng, Y., Wei, N. & MacDonald, A. H. Layer pseudospin magnetism in a transition metal dichalcogenide double-moiré system. Phys. Rev. B 106, 165105 (2022).
Yu, L. et al. Observation of quadrupolar and dipolar excitons in a semiconductor heterotrilayer. Nat. Mater. https://doi.org/10.1038/s41563-023-01678-y (2023).
Zomer, P., Guimarães, M., Brant, J., Tombros, N. & Van Wees, B. Fast pick up technique for high quality heterostructures of bilayer graphene and hexagonal boron nitride. Appl. Phys. Lett. 105, 013101 (2014).
Kim, K. et al. Van der Waals heterostructures with high accuracy rotational alignment. Nano Lett. 16, 1989–1995 (2016).
Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Klimeš, J., Bowler, D. R. & Michaelides, A. Van der Waals density functionals applied to solids. Phys. Rev. B 83, 195131 (2011).
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.
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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.
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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.
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.
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Supplementary Information
Supplementary Figs. 1–13 and Notes 1–3.
Supplementary Code 1
Calculations of model in Extended Data Fig. 1.
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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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DOI: https://doi.org/10.1038/s41563-023-01667-1
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