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Dipolar excitonic insulator in a moiré lattice

Nature Physics volume 18, pages 395–400 (2022)Cite this article

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Abstract

Two-dimensional moiré materials provide a highly controllable solid-state platform for studies of quantum phenomena1,2,3. To date, experimental studies have focused on correlated electronic states, whereas correlated bosonic states in moiré materials have received less attention. Here we report the observation of a correlated dipolar excitonic insulator—a charge-insulating state driven by exciton formation4—in a device where a WSe2 monolayer and WSe2/WS2 moiré bilayer are coupled via Coulomb interactions. The system is a Mott insulator when all the holes reside in the moiré layer. Under an out-of-plane electric field, the holes can be continuously transferred to the WSe2 monolayer, but remain strongly bound to the empty moiré sites, effectively forming an interlayer exciton fluid in the moiré lattice. We further observe the emergence of local magnetic moments in the WSe2 monolayer induced by the strong interlayer Coulomb correlation. Our result provides a platform for realizing correlated quantum phenomena described by bosonic lattice models in a solid-state system, complementary to cold-atom setups5.

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Fig. 1: Semiconductor heterostructures for realization of a dipolar exciton fluid in a lattice.
Fig. 2: Optical responses under an out-of-plane electric field.
Fig. 3: Excitonic insulator at ν = 1.
Fig. 4: Emergence of local magnetic moments in monolayer WSe2.

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Data availability

Source data are provided with this paper. Additional data that support the findings of this study are available from the corresponding authors upon reasonable request.

Code availability

The code that supports the plots within this paper is available from the corresponding authors upon reasonable request.

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Acknowledgements

This study was supported by the US Office of Naval Research under award no. N00014-21-1-2471 (capacitance measurement); the Air Force Office of Scientific Research under award no. FA9550-18-1-0480 (device fabrication); the National Science Foundation (NSF) under DMR-2004451 (data analysis); and the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award nos. DE-SC0022058 (optical measurement) and DE-SC0019481 (bulk crystal growth). The growth of hBN crystals was supported by the Elemental Strategy Initiative of MEXT, Japan, and CREST (JPMJCR15F3), JST. This work made use of the Cornell NanoScale Facility, an NNCI member supported by NSF grant NNCI-1542081.

Author information

Authors and Affiliations

  1. School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA

    Jie Gu, Liguo Ma, Jie Shan & Kin Fai Mak

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

    Song Liu & James C. Hone

  3. National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe & Takashi Taniguchi

  4. Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, USA

    Jie Shan & Kin Fai Mak

  5. Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY, USA

    Jie Shan & Kin Fai Mak

Authors
  1. Jie Gu
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Contributions

J.G. fabricated the devices, performed the optical measurements and analysed the data. J.G. and L.M. performed the capacitance measurements and analysed the compressibility data. S.L. and J.C.H. grew the bulk WSe2 crystals. K.W. and T.T. grew the bulk hBN crystals. J.G., J.S. and K.F.M. designed the scientific objectives and oversaw the project. All the authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Jie Shan or Kin Fai Mak.

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Nature Physics thanks Andrea Perali 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 Optical micrograph of device 1.

The constituent layers are outlined by lines of different colors and labeled. The effective device area is shaded in grey. The scale bar is 10 μm.

Extended Data Fig. 2 PL spectrum at different hole doping densities.

The data corresponds to the data in Fig. 1f at E = - 34 mV/nm. The spectra are vertically displaced for clarity. The left axis denotes the scale bar for the PL intensity. The right axis denotes the hole doping density for each vertically displaced spectrum. An abrupt energy shift is observed at ν = 1.

Source data

Extended Data Fig. 3 MCD spectrum as a function of magnetic field at ν = 1 and two representative electric fields.

The spectra focus on the attractive and repulsive polaron resonances of the 1 s exciton of the WSe2 monolayer. The MCD is enhanced at the resonances. The box shows the spectral window, over which the MCD is integrated. The magnetic-field dependence of the integrated MCD is shown in Fig. 4 of the main text.

Source data

Extended Data Fig. 4 Capacitance measurements.

a. Schematic of device structure and electrical connections for the AC capacitance measurement. b-d. Differential capacitance (b), PL peak intensity of the moiré layer (c), and 1 s exciton peak reflection contrast of the monolayer (d) as a function of doping density and electric field (ν, E). Electrostatic doping region III and IV in b are determined by the optical responses in c and d. A charge-incompressible state is observed at ν = 1 in region III, which weakens with increasing electric field. The dashed line in c marks the onset of doping into the moiré layer; it separates region III and IV. The black and green dashed line in d mark the onset of charging into the monolayer and in the device, respectively.

Source data

Extended Data Fig. 5 Temperature dependence of differential capacitance.

Differential bottom-gate capacitance as a function of (ν, E) at 20 K (a), 40 K (b), 60 K (c), 80 K (d), 120 K (e), and 150 K (f). The charge-incompressible state at ν = 1 disappears around 120 K.

Source data

Extended Data Fig. 6 Electrostatics phase diagram.

a-c. PL peak intensity of the moiré layer (a) and reflection peak intensity of the 1 s exciton (b) and the attractive polaron (c) of the monolayer as a function of doping density and out-of-plane electric field (ν, E). The PL arises from recombination of the interlayer excitons in the moiré bilayer. The dashed lines are the boundaries that separate the different electrostatic doping regions (labeled in d) and are determined from the optical responses. The data in a-c are well correlated with one another. d. A schematic of the electrostatics phase diagram of the TMD heterostructure as described in Methods.

Source data

Extended Data Fig. 7 PL signatures of excitonic insulator.

The PL peak intensity (a) and peak energy (b) of the WSe2/WS2 interlayer moiré excitons as a function of doping density and out-of-plane electric field (ν, E). The different electrostatic doping regions are labeled. The feature at ν = 1 in region III corresponds to the correlated excitonic insulating state. c. Doping dependence of the PL peak energy at varying electric fields. The abrupt energy shift at ν = 1 reflects a chemical potential jump for the correlated insulating state. The energy shift disappears above the critical field value around 30 mV/nm, at which the exciton Mott density (approximately 0.7 moiré density) is reached. d. Dependence of the PL peak shift at ν = 1 as a function of electric field (bottom axis) and exciton density in the units of the moiré density (top axis). The Mott density is consistent with the value from the capacitance measurement. The smaller electric-field range here is due to a thicker hBN spacer compared to the capacitance device.

Source data

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Source data for Extended Data Fig. 7.

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Gu, J., Ma, L., Liu, S. et al. Dipolar excitonic insulator in a moiré lattice. Nat. Phys. 18, 395–400 (2022). https://doi.org/10.1038/s41567-022-01532-z

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