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Intercell moiré exciton complexes in electron lattices


Excitons, Coulomb-bound electron–hole pairs, play a crucial role in both optical excitation and correlated phenomena in solids. When excitons interact with other quasiparticles, few- and many-body excited states can appear. Here we report an interaction between exciton and charges enabled by unusual quantum confinement in two-dimensional moiré superlattices, which results in many-body ground states composed of moiré excitons and correlated electron lattices. In an H-stacked (60o-twisted) WS2/WSe2 heterobilayer, we found an interlayer moiré exciton whose hole is surrounded by its partner electron’s wavefunction distributed among three adjacent moiré traps. This three-dimensional excitonic structure enables large in-plane electrical quadrupole moments in addition to the vertical dipole. Upon doping, the quadrupole facilitates the binding of interlayer moiré excitons to the charges in neighbouring moiré cells, forming intercell charged exciton complexes. Our work provides a framework for understanding and engineering emergent exciton many-body states in correlated moiré charge orders.

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Fig. 1: Spatial charge distribution of interlayer moiré exciton.
Fig. 2: Moiré exciton PL in the presence of correlated charge orders.
Fig. 3: Schematics of intercell moiré exciton complexes.
Fig. 4: Stacking-dependent moiré exciton valley polarization.

Data availability

Source data are provided with this paper. All other datasets generated during and/or analysed during this study are available from the corresponding author upon reasonable request. The DFT calculations presented in the paper were carried out using publicly available electronic structure codes (referenced in Methods). Source data are provided with this paper.


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Research on the exciton many-body ground states is mainly supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under award DE-SC0018171. Measurements on the R-stacked moiré superlattice are supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the US DOE BES, under award DE-SC0019443. The first-principles calculation is mainly supported by NSF MRSEC DMR-1719797. Computational resources were provided by HYAK at the University of Washington. The theoretical analysis and modelling effort is supported by DOE DE-SC0012509. Device fabrication is partially supported by the Army Research Office (ARO) Multidisciplinary University Research Initiative (MURI) programme (grant number W911NF-18-1-0431). The AFM-related measurements were performed using instrumentation supported by the US National Science Foundation through the UW Molecular Engineering Materials Center (MEM-C), a Materials Research Science and Engineering Center (DMR-1719797). W.Y. acknowledges support by the University Grants Committee/Research Grant Council of Hong Kong SAR (AoE/P-701/20, HKU SRFS2122-7S05) and the Tencent Foundation. Bulk WSe2 crystal growth and characterization by J.Y. is supported by the US DOE BES, Materials Sciences and Engineering Division. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan (grant number JPMXP0112101001) and JSPS KAKENHI (grant numbers 19H05790, 20H00354 and 21H05233). T.C. acknowledges support from the Micron Foundation. X.X. acknowledges support from the State of Washington-funded Clean Energy Institute and from the Boeing Distinguished Professorship in Physics. W.G.H. was supported by the NSF Graduate Research Fellowship Program under grant number DGE-1762114.

Author information

Authors and Affiliations



X.X., W.Y., T.C. and D.X. conceived the project. X.W., H.P. and J.Z. fabricated and characterized the samples. X.W., J.Z., H.P. and Y.W. performed the measurements, assisted by W.G.H. X.W., X.Z., C.W., X.X., W.Y., T.C., D.X. and D.R.G. analysed and interpreted the results. X.Z. and C.W. performed density function calculations. T.T. and K.W. synthesized the hBN crystals. J.Y. synthesized and characterized the bulk WSe2 crystals. X.X., X.W., X.Z., W.Y., T.C., D.X. and D.R.G. wrote the paper with input from all authors. All authors discussed the results.

Corresponding authors

Correspondence to Wang Yao, Di Xiao, Ting Cao or Xiaodong Xu.

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Nature Materials thanks Paulina Plochocka 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 Calculated normal strain distribution and structural energy of the R- and H-stacked heterobilayers.

a, and d, Calculated strain maps of the moiré unit cell for the fully relaxed W lattice in WS2 and WSe2 layers versus free-standing layers for (a) R- and (d) H-stacked heterolayers. b, and e, similar to a and d, but for the fully relaxed Se or S lattice in the moiré unit cell. The strain distributions are different in R- and H-stacked heterobilayers. Taking A site as the inversion center of the strain distribution as an example, the inversion symmetry weakly breaks in the former, but strongly breaks in the latter. c and f, Calculated structural energy distribution for the local stacking configuration in the moiré cell for (c) R-stacked and (f) H-stacked heterobilayers. The different structural energy distributions of local stackings lead to the distinct strain features in a-b, d-e.

Extended Data Fig. 2 Moiré filling factor assignment.

a-b, PFM image of Device R1 (a) and Device H1 (b) described in the maintext. The moiré wavelengths are measured as 7.5 nm (R1) and 8 nm (H1). c, Gate-dependent interlayer exciton photoluminescence, taken at a different cool down compared to Fig. 2d in the maintext. The excitation energy is 1.96 eV with the power 50 nW. Temperature is 4.7 K. d, Corresponding differential optical reflectance spectra of Device R1. c and d share the same y axis. e, Gate-dependent interlayer exciton PL (same as Fig. 4c) of Device H1, and f, Corresponding differential optical reflectance spectra differentiated with respect to photon energy. e and f share the same y axis.

Extended Data Fig. 3 Interlayer exciton PL of Device R1 at selected filling factors.

a, Zoom-in of gate-dependent interlayer exciton PL of Device R1 with |v| < 1. b, Linecuts of PL spectra with fractional fillings. The PL spectra are evenly offset. At hole doping side, the PL counts are multiplied by 5 times. There is little variation of PL peak energy as v varies. c, Gate-dependent interlayer exciton PL of Device R1, same as Fig. 2d in main text. d, Linecuts of PL spectra at integer filling conditions. The spectra are evenly offset. The PL counts are multiplied by either 20 or 50 times, as indicated in the plot, except at v = 0.

Extended Data Fig. 4

Relative energy shifts of PL peaks at fractional and integer fillings, with respect to charge neutrality for Device R1 (a) and Device H1 (b).

Extended Data Fig. 5 Additional R-stacked heterobilayer Device R2.

a, AFM morphology and b, PFM image of Device R2, showing the moiré wavelength is about 7.5 nm. c. Gate-dependent interlayer exciton photoluminescence of Device R2, with filling factors indicated.

Extended Data Fig. 6 Polarization resolved PL of an additional R-stacked heterobilayer Device R3.

a, Co-circularly b, cross-circularly polarized interlayer exciton PL for Device R3 under σ+ circularly polarized excitation. The excitation power is 60 nW with excitation energy 1.682 eV at 10 K. c, Corresponding degree of circularly polarization ρ. a-c share the same y axis. d, Extracted PL peak energies (dots) for each integer and fractionally filled correlated charge states. The dashed lines indicate PL peak energies at all measured gate voltages. Devices R3 and H2 (Extended Data Fig. 8) are different parts of the same sample.

Extended Data Fig. 7 PL spectra of Device H1 at select filling factors.

a, Zoom-in of gate-dependent interlayer exciton PL with |v| < 1. b, Linecuts of PL spectra at fractional filling conditions as marked. c, Gate-dependent interlayer exciton PL, same as Fig. 2f in main text. d, Linecuts of PL spectra at integer and select fractional fillings. The spectra in b and d are evenly offset for clarity. The numbers of charge carriers required to form adjacent charge orders with fractional filling factors are close. At the transition regime between two adjacent charge orders, it is possible that domains with different charge orders form. The charge order domains may be responsible for the observed multiple peaks in spectra at certain doping conditions.

Extended Data Fig. 8 Polarization resolved PL of an additional H-stacked heterobilayer Device H2.

a, Co-circularly b, cross-circularly polarized interlayer exciton PL for Device H2 under σ + circularly polarized excitation. The excitation power is 60 nW with excitation energy 1.682 eV at 10 K. c, Corresponding degree of circularly polarization ρ. ac share the same y axis. d, Extracted PL peak energies (dots) for each integer and fractionally filled correlated charge states. The dashed lines indicate PL peak energies at all measured gate voltages. Devices R3 (Extended Data Fig. 6) and H2 are different parts of the same sample.

Extended Data Fig. 9 Calculated Coulomb interaction energy between the exciton and electron-lattice for the filling factors ≤1/3.

Standard Ewald summation technique is used to calculate the Coulomb interaction energies for different filling factors. The convergence parameters have been carefully tested when doing the summation. The collective interaction is repulsive for R stacking and attractive for H stacking.

Extended Data Fig. 10 Polarization resolved PL of Device R1 at a magnetic field of 8 T.

a, Co-circularly and b, Cross-circularly polarized interlayer exciton PL under σ+ circularly polarized pump. c, The corresponding degree of circularly polarization ρ. Data is taken at 15 K. The optical excitation power is 300 nW with excitation energy at 1.678 eV.

Supplementary information

Supplementary Information

Supplementary text, Tables 1–4 and Figs. 1–3.

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Source Data Fig. 1

Input files for computational results.

Source Data Fig. 2

Statistical source data.

Source Data Fig. 4

Statistical source data.

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Wang, X., Zhang, X., Zhu, J. et al. Intercell moiré exciton complexes in electron lattices. Nat. Mater. (2023).

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