Abstract
Moiré superlattices formed by van der Waals materials can support a wide range of electronic phases, including Mott insulators1,2,3,4, superconductors5,6,7,8,9,10 and generalized Wigner crystals2. When excitons are confined by a moiré superlattice, a new class of exciton emerges, which holds promise for realizing artificial excitonic crystals and quantum optical effects11,12,13,14,15,16. When such moiré excitons are coupled to charge carriers, correlated states may arise. However, no experimental evidence exists for charge-coupled moiré exciton states, nor have their properties been predicted by theory. Here we report the optical signatures of trions coupled to the moiré potential in tungsten diselenide/molybdenum diselenide heterobilayers. The moiré trions show multiple sharp emission lines with a complex charge-density dependence, in stark contrast to the behaviour of conventional trions. We infer distinct contributions to the trion emission from radiative decay in which the remaining carrier resides in different moiré minibands. Variation of the trion features is observed in different devices and sample areas, indicating high sensitivity to sample inhomogeneity and variability. The observation of these trion features motivates further theoretical and experimental studies of higher-order electron correlation effects in moiré superlattices.
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Data availability
The data that support the findings of this study are available from the corresponding author upon request.
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Acknowledgements
We thank S. A. McGill for assistance in the magneto-optical experiments, C. T. Liang for assistance with numerical calculation, M. M. Altaiary for assistance with device fabrication, and H. W. K. Tom for equipment support. C.H.L. acknowledges support from the National Science Foundation (NSF) Division of Materials Research CAREER Award No. 1945660 and from the American Chemical Society Petroleum Research Fund No. 61640-ND6. N.M.G. acknowledges support from NSF Division of Materials Research CAREER Award No. 1651247 and from the Army Research Office Electronic Division Award No. W911NF2110260. Y.-T.C. acknowledges support from NSF under award DMR-2004701. Spectroscopic measurements at Stanford/SLAC were supported by the US Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences (BES), Materials Sciences and Engineering Division under FWP 100459 and by the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant number GBMF9462 for analysis. E.B. acknowledges partial support from Natural Sciences and Engineering Research Council (NSERC) of Canada through a PGS-D fellowship (PGSD3-502559-2017). Y.-C.C. acknowledges support from the Ministry of Science and Technology (Taiwan) under grant numbers 108-2112-M-001-041 and 109-2112-M-001-046. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan and the CREST (JPMJCR15F3), JST. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative Agreement No. DMR-1644779 and the State of Florida.
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E.L. fabricated the devices. E.L., E.B., J.v.B. and M.W. carried out the experiments. E.L. analysed the data. T.T. and K.W. provided boron nitride crystals for device fabrication. C.H.L., N.M.G. and Y.-T.C. supported the research of E.L. Y.-C.C. performed the theoretical calculations. T.F.H. supervised the research of E.B. and contributed to the interpretation of the data. C.H.L. supervised the research and coordinated the work. C.H.L., E.L., Y.-C.C. and T.F.H. wrote the manuscript with input from the other authors.
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Extended data figures and tables
Extended Data Fig. 1 Superlattice effect on the conductivity spectra of excitons and trions in the WSe2/MoSe2 heterobilayer.
a, b, Gate-dependent maps of sheet conductivity, σ (a) and its second energy derivative, d2σ/dE2 (b) of a BN-encapsulated monolayer WSe2 device. The A exciton (A0) and trions (A+ and \({{\rm{A}}}_{1,2}^{-}\)) are denoted. c, d, Similar maps for the WSe2/MoSe2 heterobilayer with a roughly 60° twist angle (device 1). The moiré A excitons (\({{\rm{MA}}}_{1,2}^{0}\)) and trions (\({{\rm{MA}}}_{1,2}^{+}\) and \({{\rm{MA}}}_{1-3}^{-}\)) are denoted. The charge neutrality (CN) regions are denoted between the dashed lines. Panels c, d share the same colour scale bar with a, b, respectively. e, Zoom-in map of the hole-side moiré trions. f, Selected spectra from e at gate voltages from −1.5 V to 0.5 V with steps of 0.25 V. The conductivity spectra are extracted from reflectance contrast, which are measured at estimated sample temperature T ≈ 15 K.
Extended Data Fig. 2 Simulation of absorption spectra of intralayer moiré exciton and trion in the WSe2/MoSe2 heterobilayer.
a, b, The experimental absorption spectra of the WSe2 intralayer exciton (a) and positive trion (b) in the WSe2/MoSe2 heterobilayer. c, d, Calculated absorption spectra of intralayer moiré exciton (c) and trion (d), broadened by a Lorentzian function with half-width of 0.5 meV and 1 meV, respectively. e, f, The calculated moiré exciton (e) and trion (f) miniband structures. The corresponding states for the absorption peaks are denoted. The calculations in c–f use a 2D sinusoidal superlattice potential with period L = 20 nm and carrier well depth V = 8 meV (inset of c).
Extended Data Fig. 3 Temperature-dependent interlayer PL in the WSe2/MoSe2 heterobilayer.
a, Temperature-dependent PL map of the interlayer exciton. We observe both the spin-singlet and spin-triplet interlayer excitons (labelled as \({{\rm{IX}}}_{{\rm{singlet}}}^{0}\) and \({{\rm{IX}}}_{{\rm{triplet}}}^{0}\), respectively), which are separated by about 25 meV. b, PL spectra at selected estimated sample temperatures. The dashed lines highlight the shift of the exciton peaks.
Extended Data Fig. 4 Power-dependent interlayer PL in the WSe2/MoSe2 heterobilayer.
a, PL map under varying incident excitation power of a 532-nm continuous laser. b, Normalized PL spectra at selected incident laser power. The sample temperature is T ≈ 5 K.
Extended Data Fig. 5 Calculated miniband structure and absorption spectra of interlayer excitons in the moiré superlattice with 2D sinusoidal model potential.
a–d, The calculated exciton minibands (a, b) and absorption spectra (c, d,) for superlattice periods L = 10, 20 and 30 nm (a, c) and L = 40 and 60 nm (b, d). Panels a, b share the same legends with c, d, respectively. The potential depth (V) of each carrier, denoted in c, d, is adjusted between 2.5 meV and 6 meV so that the exciton ground state lies at about 4 meV below the potential maximum (0 meV) to match our observation that the lowest moiré exciton line is about 4 meV below the free-exciton line (Fig. 2b). Our calculations use a total exciton effective mass m* = 0.91m0, where m0 is the free electron mass. The inset in d shows the calculated moiré period as a function of twist angle near the perfect alignment (that is, 0° or 60° twist angle), by using lattice constants of 0.3282 nm for the WSe2 and 0.3288 nm for the MoSe2 layer50.
Extended Data Fig. 6 Calculated repulsion energy between two interlayer excitons as a function of interexciton separation in the WSe2/MoSe2 heterobilayer.
The inset illustrates two interlayer excitons in the WSe2/MoSe2 heterobilayer.
Extended Data Fig. 7 Zeeman-splitting g-factors of the interlayer excitons in WSe2/MoSe2 heterobilayers.
a, b, The g-factors predicted by a single-particle model for WSe2/MoSe2 heterobilayers with 0° (a) and 60° (b) twist angle. The Zeeman-shift g-factor of a band is contributed by the spin, atomic orbit and Berry curvature, whose component g-factor is denoted, respectively, by the first, second and third numbers near the band. The sum of these three numbers is the g-factor of the band. The Zeeman-shift g-factor of an exciton equals the difference between the g-factors of the associated conduction and valence bands. The g-factor difference between an exciton and its time-reversal partner (that is, the exciton with opposite valley configurations) is the Zeeman-splitting g-factor of the exciton. Our single-particle model predicts a Zeeman-splitting g-factor of g = 4.68 for the interlayer excitons in the WSe2/MoSe2 heterobilayer with 0° twist angle, and g = 12.34 and g = 16.84, respectively, for the spin-singlet and spin-triplet interlayer excitons in the WSe2/MoSe2 heterobilayer with 60° twist angle (denoted at the bottom of each panel).
Extended Data Fig. 8 Gate-dependent PL maps of the WSe2/MoSe2 heterobilayer at zero and finite magnetic field.
a, The PL map at magnetic field B = 0 T. b, The PL map at B = 17 T. The incident laser power is P = 20 nW. The sample temperature is T ≈ 5 K. Panels a and b share the same colour scale with a. The photon energy in b is higher than that in a due to the Zeeman shift. The dashed lines approximately highlight different charging regimes.
Extended Data Fig. 9 Differential reflectance contrast maps for two different WSe2/MoSe2 heterobilayer devices.
a, b, The gate-dependent maps of the second-order energy derivative of reflectance contrast for device 1 (a; twist angle of roughly 60°) and device 5 (b; twist angle of roughly 0°). The map in a corresponds to Fig. 2d. Similar split exciton and trion features are observed in both devices. However, although \({{\rm{MA}}}_{2}^{+}\) is weaker than \({{\rm{MA}}}_{1}^{+}\) in the roughly 60° heterobilayer, \({{\rm{MA}}}_{2}^{+}\) is stronger than \({{\rm{MA}}}_{1}^{+}\) in the roughly 0° heterobilayer. Moreover, the energy separation between \({{\rm{MA}}}_{1}^{+}\) and \({{\rm{MA}}}_{2}^{+}\) is slightly larger in the roughly 0° heterobilayer (10.7 meV) than in the roughly 60° heterobilayer (9.3 meV). These differences may be induced by the different potential depths of the roughly 0° and roughly 60° heterobilayers. c, A similar map at a different sample position of device 1. The variation indicates the spatial inhomogeneity of the sample. The sample temperature is estimated to be T ≈ 15 K in these measurements.
Extended Data Fig. 10 Gate-dependent PL maps for different WSe2/MoSe2 heterobilayer devices.
a–l, High-excitation-power PL maps (a, d, g, j), low-excitation-power PL maps (b, e, h, k) and cross-cut spectra (c, f, i, l) of device 2 (a–c), device 3 (d–f), device 4 (g–i) and device 5 (j–l). Devices 2, 3 and 4 have approximately 60° twist angles; device 5 has an approximately 0° twist angle. The panels denote the incident laser power, the free interlayer exciton and trion emission (IX0 and IX±) and their associated moiré exciton emission (MX0 and MX±). A Stark shift is observed in the interlayer trion PL of device 5 because it is a single-gate device, in which charge injection induces an interlayer electric field, whereas devices 2–4 are dual-gate devices that allow us to inject carriers without applying an electric field to the heterobilayer. Sharp trion lines are observed in all of these devices, signifying the emergence of moiré trions. The sample temperature is T ≈ 5 K for the PL measurements of devices 2 and 3 and T ≈ 1.7 K for the PL measurements of devices 4 and 5.
Supplementary information
Supplementary Information
This Supplementary Information contains the following sections: (1) Theory of intralayer and interlayer excitons in the WSe2/MoSe2 heterobilayer; (2) Theory of intralayer and interlayer trions in the WSe2/MoSe2 heterobilayer; (3) Calculation of moiré exciton minibands and absorption spectra; (4) Calculation of the absorption and emission spectra of moiré trions; and (5) Calculation of the exciton-exciton repulsion energy in moiré potential well.
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Liu, E., Barré, E., van Baren, J. et al. Signatures of moiré trions in WSe2/MoSe2 heterobilayers. Nature 594, 46–50 (2021). https://doi.org/10.1038/s41586-021-03541-z
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DOI: https://doi.org/10.1038/s41586-021-03541-z
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