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.

# Electrically tunable quantum confinement of neutral excitons

## Abstract

Confining particles to distances below their de Broglie wavelength discretizes their motional state. This fundamental effect is observed in many physical systems, ranging from electrons confined in atoms or quantum dots1,2 to ultracold atoms trapped in optical tweezers3,4. In solid-state photonics, a long-standing goal has been to achieve fully tunable quantum confinement of optically active electron–hole pairs, known as excitons. To confine excitons, existing approaches mainly rely on material modulation5, which suffers from poor control over the energy and position of trapping potentials. This has severely impeded the engineering of large-scale quantum photonic systems. Here we demonstrate electrically controlled quantum confinement of neutral excitons in 2D semiconductors. By combining gate-defined in-plane electric fields with inherent interactions between excitons and free charges in a lateral p–i–n junction, we achieve exciton confinement below 10 nm. Quantization of excitonic motion manifests in the measured optical response as a ladder of discrete voltage-dependent states below the continuum. Furthermore, we observe that our confining potentials lead to a strong modification of the relative wave function of excitons. Our technique provides an experimental route towards creating scalable arrays of identical single-photon sources and has wide-ranging implications for realizing strongly correlated photonic phases6,7 and on-chip optical quantum information processors8,9.

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

## Access options

\$32.00

All prices are NET prices.

## Data availability

The data that support the findings of this study will be made publicly available at the ETH Research Collection on publication (http://hdl.handle.net/20.500.11850/478320).

## References

1. Hawrylak, P. & Korkusiński, M. in Single Quantum Dots: Fundamentals, Applications, and New Concepts (ed. Michler, P.) 25–92 (Springer, 2003).

2. Harrison, P. & Valavanis, A. Quantum Wells, Wires and Dots: Theoretical and Computational Physics of Semiconductor Nanostructures 241–265 (Wiley, 2016).

3. Serwane, F. et al. Deterministic preparation of a tunable few-fermion system. Science 332, 336–338 (2011).

4. Kaufman, A. M., Lester, B. J. & Regal, C. A. Cooling a single atom in an optical tweezer to its quantum ground state. Phys. Rev. X 2, 041014 (2012).

5. Davies, J. H. The Physics of Low-dimensional Semiconductors 118–129 (Cambridge Univ. Press, 1997).

6. Carusotto, I. & Ciuti, C. Quantum fluids of light. Rev. Mod. Phys. 85, 299–366 (2013).

7. Noh, C. & Angelakis, D. G. Quantum simulations and many-body physics with light. Rep. Prog. Phys. 80, 016401 (2016).

8. O’Brien, J. L., Furusawa, A. & Vučković, J. Photonic quantum technologies. Nat. Photonics 3, 687–695 (2009).

9. Aspuru-Guzik, A. & Walther, P. Photonic quantum simulators. Nat. Phys. 8, 285–291 (2012).

10. Hagn, M., Zrenner, A., Böhm, G. & Weimann, G. Electric-field-induced exciton transport in coupled quantum well structures. Appl. Phys. Lett. 67, 232 (1995).

11. Rapaport, R. et al. Electrostatic traps for dipolar excitons. Phys. Rev. B 72, 075428 (2005).

12. Gärtner, A., Prechtel, L., Schuh, D., Holleitner, A. W. & Kotthaus, J. P. Micropatterned electrostatic traps for indirect excitons in coupled GaAs quantum wells. Phys. Rev. B 76, 085304 (2007).

13. Vögele, X. P., Schuh, D., Wegscheider, W., Kotthaus, J. P. & Holleitner, A. W. Density enhanced diffusion of dipolar excitons within a one-dimensional channel. Phys. Rev. Lett. 103, 126402 (2009).

14. Schinner, G. J. et al. Confinement and interaction of single indirect excitons in a voltage-controlled trap formed inside double InGaAs quantum wells. Phys. Rev. Lett. 110, 127403 (2013).

15. Butov, L. V. Excitonic devices. Superlattices Microstruct. 108, 2–26 (2017).

16. Hammack, A. T. et al. Excitons in electrostatic traps. J. Appl. Phys. 99, 066104 (2006).

17. Unuchek, D. et al. Room-temperature electrical control of exciton flux in a van der Waals heterostructure. Nature 560, 340–344 (2018).

18. Wang, G. et al. Colloquium: Excitons in atomically thin transition metal dichalcogenides. Rev. Mod. Phys. 90, 021001 (2018).

19. Liu, Y. et al. Electrically controllable router of interlayer excitons. Sci. Adv. 6, 1830 (2020).

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

21. Shanks, D. N. et al. Nanoscale trapping of interlayer excitons in a 2D semiconductor heterostructure. Nano Lett. 21, 5641–5647 (2021).

22. Goryca, M. et al. Revealing exciton masses and dielectric properties of monolayer semiconductors with high magnetic fields. Nat. Commun. 10, 4172 (2019).

23. Cavalcante, L. S., Da Costa, D. R., Farias, G. A., Reichman, D. R. & Chaves, A. Stark shift of excitons and trions in two-dimensional materials. Phys. Rev. B 98, 245309 (2018).

24. Efimkin, D. K. & MacDonald, A. H. Many-body theory of trion absorption features in two-dimensional semiconductors. Phys. Rev. B 95, 035417 (2017).

25. Sidler, M. et al. Fermi polaron-polaritons in charge-tunable atomically thin semiconductors. Nat. Phys. 13, 255–261 (2017).

26. Chervy, T. et al. Accelerating polaritons with external electric and magnetic fields. Phys. Rev. 10, 011040 (2020).

27. Wang, J. Highly polarized photoluminescence and photodetection from single indium phosphide nanowires. Science 293, 1455–1457 (2001).

28. Akiyama, H., Someya, T. & Sakaki, H. Optical anisotropy in 5-nm-scale T-shaped quantum wires fabricated by the cleaved-edge overgrowth method. Phys. Rev. B 53, 4229–4232 (1996).

29. Lefebvre, J., Fraser, J. M., Finnie, P. & Homma, Y. Photoluminescence from an individual single-walled carbon nanotube. Phys. Rev. B 69, 075403 (2004).

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

31. Wang, Q. et al. Highly polarized single photons from strain-induced quasi-1D localized excitons in WSe2. Nano Lett. 21, 7175–7182 (2021).

32. Glazov, M. M. et al. Spin and valley dynamics of excitons in transition metal dichalcogenide monolayers. Phys. Status Solidi B 252, 2349–2362 (2015).

33. Yu, H., Cui, X., Xu, X. & Yao, W. Valley excitons in two-dimensional semiconductors. Natl Sci. Rev. 2, 57–70 (2015).

34. Nagamune, Y. et al. Photoluminescence spectra and anisotropic energy shift of GaAs quantum wires in high magnetic fields. Phys. Rev. Lett. 69, 2963–2966 (1992).

35. Togan, E., Lim, H.-T., Faelt, S., Wegscheider, W. & Imamoglu, A. Enhanced interactions between dipolar polaritons. Phys. Rev. Lett. 121, 227402 (2018).

36. Lim, H.-T., Togan, E., Kroner, M., Miguel-Sanchez, J. & Imamoglu, A. Electrically tunable artificial gauge potential for polaritons. Nat. Commun. 8, 14540 (2017).

37. Chestnov, I. Y., Arakelian, S. M. & Kavokin, A. V. Giant synthetic gauge field for spinless microcavity polaritons in crossed electric and magnetic fields. New J. Phys. 23, 023024 (2021).

38. 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).

39. Kremser, M. et al. Discrete interactions between a few interlayer excitons trapped at a MoSe2–WSe2 heterointerface. NPJ 2D Mater. Appl. 4, 8 (2020).

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

41. Rosenberg, I. et al. Strongly interacting dipolar-polaritons. Sci. Adv. 4, eaat8880 (2018).

42. Lodahl, P., Mahmoodian, S. & Stobbe, S. Interfacing single photons and single quantum dots with photonic nanostructures. Rev. Mod. Phys. 87, 347–400 (2015).

43. Carusotto, I. et al. Fermionized photons in an array of driven dissipative nonlinear cavities. Phys. Rev. Lett. 103, 033601 (2009).

44. Ołdziejewski, R., Chiocchetta, A., Knörzer, J. & Schmidt, R. Excitonic Tonks-Girardeau and charge-density wave phases in monolayer semiconductors. Preprint at https://arxiv.org/abs/2106.07290 (2021).

45. Hartmann, M. J., Brandao, F. G. & Plenio, M. B. Strongly interacting polaritons in coupled arrays of cavities. Nat. Phys. 2, 849–855 (2006).

46. Greentree, A. D., Tahan, C., Cole, J. H. & Hollenberg, L. C. Quantum phase transitions of light. Nat. Phys. 2, 856–861 (2006).

47. Zomer, P. J., Guimarães, M. H. D., Brant, J. C., Tombros, N. & van Wees, B. J. Fast pick up technique for high quality heterostructures of bilayer graphene and hexagonal boron nitride. Appl. Phys. Lett. 105, 013101 (2014).

48. Telford, E. J. et al. Via method for lithography free contact and preservation of 2D materials. Nano Lett. 18, 1416–1420 (2018).

49. Jung, Y. et al. Transferred via contacts as a platform for ideal two-dimensional transistors. Nat. Electron. 2, 187–194 (2019).

50. Wilson, N. R. et al. Determination of band offsets, hybridization, and exciton binding in 2D semiconductor heterostructures. Sci. Adv. 3, 1601832 (2017).

51. Larentis, S. et al. Large effective mass and interaction-enhanced Zeeman splitting of K-valley electrons in MoSe2. Phys. Rev. B 97, 201407 (2018).

52. Zhang, Y. et al. Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2. Nat. Nanotechnol. 9, 111–115 (2014).

53. Laturia, A., de Put, M. L. V. & Vandenberghe, W. G. Dielectric properties of hexagonal boron nitride and transition metal dichalcogenides: from monolayer to bulk. NPJ 2D Mater. Appl. 2, 6 (2018).

54. Smoleński, T. et al. Interaction-induced Shubnikov–de Haas oscillations in optical conductivity of monolayer MoSe2. Phys. Rev. Lett. 123, 097403 (2019).

55. Scuri, G. et al. Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride. Phys. Rev. Lett. 120, 037402 (2018).

56. Lozovik, Y. E., Ovchinnikov, I. V., Volkov, S. Y., Butov, L. V. & Chemla, D. S. Quasi-two-dimensional excitons in finite magnetic fields. Phys. Rev. B 65, 235304 (2002).

## Acknowledgements

We thank A. Srivastava, I. Schwartz, R. Schmidt, A. Bergschneider and N. Lassaline for insightful discussions. This work was produced within the scope of the National Research Programme NCCR QSIT, which was financed by the Swiss National Science Foundation (SNSF) and supported by the SNSF grant 200021-178909/1. P.A.M. acknowledges financing from the European Union’s Horizon 2020 programme under Marie Skłodowska-Curie grant MSCA-IF-OptoTransport (843842). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan, A3 Foresight by JSPS and CREST (grant number JPMJCR15F3) and JST. D.T. and D.J.N. acknowledge support by the SNSF under grant 200021-165559. T.C. acknowledges support from NTT Research, Inc., USA. Synthesis of MoSe2 crystals in Device 2 was supported by the United States National Science Foundation Materials Research Science and Engineering Centers DMR-2011738.

## Author information

Authors

### Contributions

P.A.M., A.I. and D.T. conceptualized the project. D.T., T.S. and P.A.M. carried out the experiments. D.T. performed the electrostatic simulations, with input from P.A.M. and A.P. D.T. fabricated Device 1 and X.L. fabricated Device 2. I.A. performed exact diagonalization calculations. A.P. assisted with measurements, device fabrication and simulations. K.W. and T.T. provided the h-BN crystals. S.L. and K.B. provided the MoSe2 crystals for Device 2. M.K. and T.C. assisted P.A.M. and D.T. with the experimental setup. P.A.M., D.T. and A.I. wrote the manuscript. A.I., D.J.N., M.K. and P.A.M. supervised the project.

### Corresponding authors

Correspondence to Atac Imamoglu or Puneet A. Murthy.

## Ethics declarations

### Competing interests

D.T., P.A.M., M.K., A.P. and A.I. are seeking patent protection for ideas described in this work.

## Peer review

### Peer review information

Nature thanks Mikhail Glazov, Libai Huang and the other, anonymous, reviewer for their contribution to the peer review of this work. Peer reviewer reports are available.

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 Electrostatic simulations of the device.

Magnitude of charge density |σ(x)|, in-plane electric field |Fx| and exciton confining potential V(x) as a function of position for varying TG voltages VTG and fixed BG voltage VBG = 4 V. The BG extends over the entire plotted range of the position from −80 nm to 80 nm. The TG extends from −80 nm to 0 nm, with the edge at x = 0. The different charging configurations, namely n–n–n (a, b), i–i–n (c, d) and p–i–n (e, f), show the evolution of the confinement potential as a function of VTG.

### Extended Data Fig. 2 Doping characteristics of Device 1.

We use the charge-density-dependent energy shifts of the repulsive polaron states to obtain the doping configuration of the device. Because the RP states exist in regions I and II of the device and on electron and hole sides, we use the notation $${{\rm{RP}}}_{{\rm{region}}}^{{\rm{charge}}}$$ to denote the different states. a, Normalized reflectance ΔR/R measured for fixed VTG = −6 V as a function of VBG, in which we mainly observe features from region I. b, ΔR/R measured for fixed VBG = 1.8 V as a function of VTG, in which we observe the spectral changes in region II. In addition to the features from region II, we see the repulsive polaron resonance from region I at E ≈ 1,648 meV, which is not affected by VTG. c, Normalized reflectance taken at a fixed energy EX0 + Γ/2 = 1,645 meV, in which Γ is the bare 2D exciton linewidth. The horizontal solid lines demarcate the n-doped, neutral and p-doped regimes in region I. The doping configurations in regions I and II in different voltage regimes are identified. For example, in the top-left corner, which is the relevant regime for this work, the doping configuration is (II, I) ≡ (p, n). d, Schematic of the device showing regions I and II, as well as the position of the electrical contact to the monolayer.

### Extended Data Fig. 3 Electrically tunable quantum confinement in Device 2.

a, Optical micrograph of Device 2, in which the outline of the MoSe2 monolayer is indicated by the red line. The TG and BG, made of few-layer graphene, are indicated by dashed black lines. b, Schematic diagram of Device 2. c, Spectra taken at the edge of the few-layer graphene TG at VBG = 1 V show the emergence of discrete states below the 2D continuum, in excellent agreement with the observations in Device 1 (Fig. 2b). d, Spectral linecuts at VTG = 0 V, −4 V and −9 V show the emergence of confined states as the potential is made deeper. The exact voltage range and the magnitude of red shift may differ between the two devices owing to design differences, in particular, the thickness of h-BN spacers.

### Extended Data Fig. 4 Quantum confinement in the n–i–p regime.

Normalized reflectance ΔR/R from Device 2 as a function of VTG for fixed VBG = −7 V, corresponding to hole doping in region I. We observe qualitatively similar signatures of quantum confinement as the p–i–n regime shown in the main text, which includes narrow discrete states emerging out of the repulsive polaron (RP) continuum for VTG 2.5 V.

### Extended Data Fig. 5 Line shape analysis of reflectance data.

a, Spectral profile described by equation (8) fit to the bare 2D exciton transition at VTG = −3.5 V. b, Reflectance linecut at VTG = −6.2 V fit by a superposition of several narrow spectral profiles $${\sum }_{i}S(E;{E}_{0,i},{\Gamma }_{i},{A}_{i},{\alpha }_{c})+S(E;{E}_{{\rm{RP}}},{\Gamma }_{{\rm{RP}}},{A}_{{\rm{RP}}},{\alpha }_{{\rm{RP}}})$$ c, Individual components of the fit. d, Individual components after removing line asymmetry by setting αc and αRP to 0°. The resulting overall line shape is shown in red. e, Results of the fitting procedure for the different resonances at VTG = −6.2 V.

### Extended Data Fig. 6 PL spectra at orthogonal polarization angles for Device 1 and Device 2.

a, In Device 1, all discrete states show linear polarized states along the edge of the gate, with a high degree of linear polarization. b, In Device 2, the confinement is weaker owing to thicker h-BN spacer layers, which leads to the observation of both x-polarized and y-polarized states with a finite energy splitting δ of around 1 meV. The unmodified resonance at E − E2D of around 0.5 meV corresponds to the repulsive polaron emission from the region under the TG.

### Extended Data Fig. 7 Linear polarization anisotropy of different optical resonances.

a, PL BG (VBG) scan conducted on bare MoSe2 away from TG region. b, c, PL TG (VTG) scan performed on the TG. df, Polarization dependence of optical transitions in regions I, II and III, which are represented in purple, magenta and orange, respectively. The exciton, hole-side attractive polaron and electron-side attractive polaron is marked with a circle, cross and dash, respectively.

### Extended Data Fig. 8 Excitation power dependence of resonance energy in PL.

a, Shift in resonance energy of X2D (blue) and XQC (black) states relative to their energy measured at the lowest excitation power. b, Evolution of energy splitting between two successive quantum-confined states with power. The shaded areas represent errors from fitting.

### Extended Data Fig. 9 Extracted g-factor and zero-field splitting.

g-Factor (a) and zero-field splitting δ as a function of TG voltage VTG (b), determined by fitting reflection spectra acquired at finite magnetic fields in the range B = 0–16 T. The shaded areas represent fitting errors.

### Extended Data Fig. 10 Exact diagonalization of exciton relative motion in crossed electric and magnetic fields.

a, Energy of the MLESO as a function of the in-plane electric field strength Fx at B = 0 T. A quadratic dependence with the electric field is observed, as expected from the dc Stark effect. b, The probability density |ψ(r = 0)|2, proportional to the exciton oscillator strength, decreases by about 10–15% with increasing electric field Fx. Hence, a decrease in oscillator strength, as seen in the experiment, should primarily arise from COM quantum confinement of excitons. c, d, Calculated probability density |ψ(r)|2 for Fx = 0 and Fx = 30 V μm−1, respectively. e, Probability density |ψ(x, y = 0)|2 in the direction of the electric field for Fx = 0 (blue) and Fx = 30 V μm−1 (red). The oscillations seen at finite electric field arise from reflections from the finite-sized box assumed in the calculations. The black curve is a guide to the eye, to show the small but finite component of the wave function that exists outside the Coulomb potential. f, MLESO energy shift with respect to the energy E(B = 0 T) as a function of B, for different values of Fx. The magnitude of the predicted shift is on the same order as in the experimental observation.

## Rights and permissions

Reprints and Permissions

Thureja, D., Imamoglu, A., Smoleński, T. et al. Electrically tunable quantum confinement of neutral excitons. Nature 606, 298–304 (2022). https://doi.org/10.1038/s41586-022-04634-z

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41586-022-04634-z