Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

# Signatures of moiré trions in WSe2/MoSe2 heterobilayers

## 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.

This is a preview of subscription content, access via your institution

## Relevant articles

• ### Exciton-polarons in the presence of strongly correlated electronic states in a MoSe2/WSe2 moiré superlattice

npj 2D Materials and Applications Open Access 04 November 2022

• ### Interactions between Fermi polarons in monolayer WS2

Nature Communications Open Access 18 October 2022

• ### Localized interlayer excitons in MoSe2–WSe2 heterostructures without a moiré potential

Nature Communications Open Access 12 September 2022

## Access options

\$32.00

All prices are NET prices.

## Data availability

The data that support the findings of this study are available from the corresponding author upon request.

## References

1. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

2. Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).

3. Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020).

4. Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moiré heterostructure. Nature 580, 472–477 (2020).

5. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

6. Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).

7. Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).

8. Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).

9. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).

10. Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).

11. Alexeev, E. M. et al. Resonantly hybridized excitons in moiré superlattices in van der Waals heterostructures. Nature 567, 81–86 (2019); correction 572, E8 (2019).

12. Jin, C. et al. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019); correction 569, E7 (2019).

13. Tran, K. et al. Evidence for moiré excitons in van der Waals heterostructures. Nature 567, 71–75 (2019).

14. Seyler, K. L. et al. Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers. Nature 567, 66–70 (2019).

15. Wu, F., Lovorn, T. & MacDonald, A. H. Topological exciton bands in moiré heterojunctions. Phys. Rev. Lett. 118, 147401 (2017).

16. Yu, H., Liu, G.-B., Tang, J., Xu, X. & Yao, W. Moiré excitons: from programmable quantum emitter arrays to spin–orbit-coupled artificial lattices. Sci. Adv. 3, e1701696 (2017).

17. Baek, H. et al. Highly energy-tunable quantum light from moiré-trapped excitons. Sci. Adv. 6, eaba8526 (2020).

18. Bai, Y. et al. Excitons in strain-induced one-dimensional moiré potentials at transition metal dichalcogenide heterojunctions. Nat. Mater. 19, 1068–1073 (2020); correction 19, 1124 (2020).

19. Jauregui, L. A. et al. Electrical control of interlayer exciton dynamics in atomically thin heterostructures. Science 366, 870–875 (2019).

20. Rivera, P. et al. Valley-polarized exciton dynamics in a 2D semiconductor heterostructure. Science 351, 688–691 (2016).

21. Rivera, P. et al. Observation of long-lived interlayer excitons in monolayer MoSe2–WSe2 heterostructures. Nat. Commun. 6, 6242 (2015).

22. Miller, B. et al. Long-lived direct and indirect interlayer excitons in van der Waals heterostructures. Nano Lett. 17, 5229–5237 (2017).

23. Yu, H., Wang, Y., Tong, Q., Xu, X. & Yao, W. Anomalous light cones and valley optical selection rules of interlayer excitons in twisted heterobilayers. Phys. Rev. Lett. 115, 187002 (2015).

24. Wu, F., Lovorn, T. & MacDonald, A. H. Theory of optical absorption by interlayer excitons in transition metal dichalcogenide heterobilayers. Phys. Rev. B 97, 035306 (2018).

25. Nagler, P. et al. Giant magnetic splitting inducing near-unity valley polarization in van der Waals heterostructures. Nat. Commun. 8, 1551 (2017).

26. Jiang, C. Y. et al. Microsecond dark-exciton valley polarization memory in two-dimensional heterostructures. Nat. Commun. 9, 753 (2018).

27. Hsu, W. T. et al. Negative circular polarization emissions from WSe2/MoSe2 commensurate heterobilayers. Nat. Commun. 9, 1356 (2018).

28. 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).

29. Calman, E. V. et al. Indirect excitons and trions in MoSe2/WSe2 van der Waals heterostructures. Nano Lett. 20, 1869–1875 (2020).

30. Wang, T. et al. Giant valley-Zeeman splitting from spin-singlet and spin-triplet interlayer excitons in WSe2/MoSe2 heterostructure. Nano Lett. 20, 694–700 (2020).

31. Yu, H., Liu, G.-B. & Yao, W. Brightened spin-triplet interlayer excitons and optical selection rules in van der Waals heterobilayers. 2D Mater. 5, 035021 (2018).

32. Wang, J. et al. Diffusivity reveals three distinct phases of interlayer excitons in MoSe2/WSe2 heterobilayers. Phys. Rev. Lett. 126, 106804 (2021).

33. Lu, X., Li, X. & Yang, L. Modulated interlayer exciton properties in a two-dimensional moiré crystal. Phys. Rev. B 100, 155416 (2019).

34. Woźniak, T., Faria, P. E. Jr, Seifert, G., Chaves, A. & Kunstmann, J. Exciton g factors of van der Waals heterostructures from first-principles calculations. Phys. Rev. B 101, 235408 (2020).

35. Brotons-Gisbert, M. et al. Moiré-trapped interlayer trions in a charge-tunable WSe2/MoSe2 heterobilayer. Preprint at https://arxiv.org/abs/2101.07747 (2021).

36. Baek, H. et al. Optical read-out of Coulomb staircases in a moiré superlattice via trapped interlayer trions. Preprint at https://arxiv.org/abs/2102.01358 (2021).

37. Liu, E. et al. Landau-quantized excitonic absorption and luminescence in a monolayer valley semiconductor. Phys. Rev. Lett. 124, 097401 (2020).

38. Wang, J. et al. Optical generation of high carrier densities in 2D semiconductor heterobilayers. Sci. Adv. 5, eaax0145 (2019).

39. Aivazian, G. et al. Magnetic control of valley pseudospin in monolayer WSe2. Nat. Phys. 11, 148–152 (2015).

40. Li, Y. et al. Valley splitting and polarization by the Zeeman effect in monolayer MoSe2. Phys. Rev. Lett. 113, 266804 (2014).

41. MacNeill, D. et al. Breaking of valley degeneracy by magnetic field in monolayer MoSe2. Phys. Rev. Lett. 114, 037401 (2015).

42. Srivastava, A. et al. Valley Zeeman effect in elementary optical excitations of monolayer WSe2. Nat. Phys. 11, 141–147 (2015).

43. Wang, G. et al. Magneto-optics in transition metal diselenide monolayers. 2D Mater. 2, 034002 (2015).

44. Rostami, H. & Asgari, R. Valley Zeeman effect and spin-valley polarized conductance in monolayer MoS2 in a perpendicular magnetic field. Phys. Rev. B 91, 075433 (2015).

45. Nguyen, P. V. et al. Visualizing electrostatic gating effects in two-dimensional heterostructures. Nature 572, 220–223 (2019).

46. Liu, E. et al. Multipath optical recombination of intervalley dark excitons and trions in monolayer WSe2. Phys. Rev. Lett. 124, 196802 (2020).

47. Andor, K. et al. k · p theory for two-dimensional transition metal dichalcogenide semiconductors. 2D Mater. 2, 022001 (2015).

48. Joe, A. Y. et al. Electrically controlled emission from singlet and triplet exciton species in atomically thin light-emitting diodes. Phys. Rev. B 103, L161411 (2021).

49. Yankowitz, M. et al. Emergence of superlattice Dirac points in graphene on hexagonal boron nitride. Nat. Phys. 8, 382–386 (2012).

50. Al-Hilli, A. A. & Evans, B. L. The preparation and properties of transition metal dichalcogenide single crystals. J. Cryst. Growth 15, 93–101 (1972).

51. Yoo, H. et al. Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene. Nat. Mater. 18, 448–453 (2019).

52. Weston, A. et al. Atomic reconstruction in twisted bilayers of transition metal dichalcogenides. Nat. Nanotechnol. 15, 592–597 (2020).

53. Rosenberger, M. R. et al. Twist angle-dependent atomic reconstruction and moiré patterns in transition metal dichalcogenide heterostructures. ACS Nano 14, 4550–4558 (2020).

54. Andersen, T. I. et al. Excitons in a reconstructed moiré potential in twisted WSe2/WSe2 homobilayers. Nat. Mater. 20, 480–487 (2021).

55. Halbertal, D. et al. Moiré metrology of energy landscapes in van der Waals heterostructures. Nat. Commun. 12, 242 (2021).

56. 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).

## 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.

## Author information

Authors

### Contributions

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.

### Corresponding authors

Correspondence to Yia-Chung Chang or Chun Hung Lui.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Qihua Xiong and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## 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 cf 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.

ad, 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.

al, 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 (ac), device 3 (df), device 4 (gi) and device 5 (jl). 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.

## Rights and permissions

Reprints and Permissions

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

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41586-021-03541-z

• ### Semiconductor moiré materials

• Kin Fai Mak
• Jie Shan

Nature Nanotechnology (2022)

• ### Interactions between Fermi polarons in monolayer WS2

• Jack B. Muir
• Jesper Levinsen
• Jeffrey A. Davis

Nature Communications (2022)

• ### Localized interlayer excitons in MoSe2–WSe2 heterostructures without a moiré potential

• Fateme Mahdikhanysarvejahany
• Daniel N. Shanks
• John R. Schaibley

Nature Communications (2022)

• ### Quantum photonics with layered 2D materials

• Mikko Turunen
• Mauro Brotons-Gisbert
• Brian D. Gerardot

Nature Reviews Physics (2022)

• ### Exciton-polarons in the presence of strongly correlated electronic states in a MoSe2/WSe2 moiré superlattice

• Aidan J. Campbell
• Mauro Brotons-Gisbert
• Brian D. Gerardot

npj 2D Materials and Applications (2022)