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Fermi edge singularity in neutral electron–hole system

Nature Physics volume 19, pages 1275–1279 (2023)Cite this article

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Abstract

In neutral dense electron–hole systems at low temperatures, theory predicted Cooper-pair-like excitons exist at the Fermi energy and form a Bardeen–Cooper–Schrieffer-like condensate. Optical excitations create electron–hole systems with the density controlled via the excitation power. However, the intense optical excitations required to achieve high densities cause substantial heating that prevents the realization of simultaneously dense and cold electron–hole systems in conventional semiconductors. Here we show that the separation of electron and hole layers enables the realization of a simultaneously dense and cold electron–hole system. We find a strong enhancement of photoluminescence intensity at the Fermi energy of the neutral dense ultracold electron–hole system that demonstrates the emergence of an excitonic Fermi edge singularity due to the formation of Cooper-pair-like excitons at the Fermi energy. Our measurements also show a crossover from the hydrogen-like excitons to the Cooper-pair-like excitons with increasing density, consistent with the theoretical prediction of a smooth transition.

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Fig. 1: I-EHP diagrams and PL spectra.
Fig. 2: The density and temperature dependence of PL spectra.
Fig. 3: The spectrum skewness M3.
Fig. 4: The coherence length at different temperatures.

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Source data files are available via Figshare66. All relevant data are available from the authors upon reasonable request.

References

  1. Keldysh, L. V. & Kozlov, A. N. Collective properties of excitons in semiconductors. Sov. Phys. JETP 27, 521–528 (1968).

    ADS  Google Scholar 

  2. Keldysh, L. V. & Kopaev, Y. V. Possible instability of the semimetallic state toward Coulomb interaction. Sov. Phys. Solid State 6, 2219–2224 (1965).

    Google Scholar 

  3. Butov, L. V., Kulakovskii, V. D., Lach, E., Forchel, A. & Grützmacher, D. Magnetoluminescence study of many-body effects in homogeneous quasi-two-dimensional electron-hole plasma in undoped InGaAs/InP single quantum wells. Phys. Rev. B 44, 10680–10688 (1991).

    Article  ADS  Google Scholar 

  4. High, A. A. et al. Indirect excitons in elevated traps. Nano Lett. 9, 2094–2098 (2009).

    Article  ADS  Google Scholar 

  5. Mahan, G. D. Excitons in degenerate semiconductors. Phys. Rev. 153, 882–889 (1967).

    Article  ADS  Google Scholar 

  6. Combescot, M. & Noziéres, P. Infrared catastrophy and excitons in the X-ray spectra of metals. J. de Phys. 32, 913–929 (1971).

    Article  Google Scholar 

  7. Skolnick, M. S. et al. Observation of a many-body edge singularity in quantum-well luminescence spectra. Phys. Rev. Lett. 58, 2130–2133 (1987).

    Article  ADS  Google Scholar 

  8. Lee, J. S., Iwasa, Y. & Miura, N. Observation of the Fermi edge anomaly in the absorption and luminescence spectra of n-type modulation-doped GaAs–AlGaAs quantum wells. Semicond. Sci. Technol. 2, 675–678 (1987).

    Article  ADS  Google Scholar 

  9. Livescu, A. et al. Free carrier and many-body effects in absorption spectra of modulation-doped quantum wells. IEEE J. Quantum Electron. 24, 1677–1689 (1988).

    Article  ADS  Google Scholar 

  10. Ohtaka, K. & Tanabe, Y. Golden-rule approach to the soft-x-ray-absorption problem. V. Thermal broadening and comparison with experiments in quantum wells. Phys. Rev. B 39, 3054–3064 (1989).

    Article  ADS  Google Scholar 

  11. Uenoyama, T. & Sham, L. J. Effect of finite hole mass on edge singularities in optical spectra. Phys. Rev. Lett. 65, 1048–1051 (1990).

    Article  ADS  Google Scholar 

  12. Hawrylak, P. Optical properties of a two-dimensional electron gas: evolution of spectra from excitons to Fermi-edge singularities. Phys. Rev. B 44, 3821–3828 (1991).

  13. Butov, L. V., Egorov, V. D., Kulakovskii, V. D. & Anderson, T. G. Magnetoluminescence study of many-body effects in a dense electron-hole plasma of strained InxGa1−xAs/GaAs quantum wells. Phys. Rev. B 46, 15156–15162 (1992).

    Article  ADS  Google Scholar 

  14. Kappei, L., Szczytko, J., Morier-Genoud, F. & Deveaud, B. Direct observation of the Mott transition in an optically excited semiconductor quantum well. Phys. Rev. Lett. 94, 147403 (2005).

    Article  ADS  Google Scholar 

  15. Lozovik, Y. E. & Yudson, V. I. A new mechanism for superconductivity: pairing between spatially separated electrons and holes. Sov. Phys. JETP 44, 389–397 (1976).

    ADS  Google Scholar 

  16. Butov, L. V. et al. Stimulated scattering of indirect excitons in coupled quantum wells: signature of a degenerate Bose-gas of excitons. Phys. Rev. Lett. 86, 5608–5611 (2001).

    Article  ADS  Google Scholar 

  17. Yoshioka, D. & MacDonald, A. H. Double quantum well electron-hole systems in strong magnetic fields. J. Phys. Soc. Jpn 59, 4211–4214 (1990).

    Article  ADS  Google Scholar 

  18. Zhu, X., Littlewood, P. B., Hybertsen, M. & Rice, T. Exciton condensate in semiconductor quantum well structures. Phys. Rev. Lett. 74, 1633–1636 (1995).

    Article  ADS  Google Scholar 

  19. Lozovik, Y. E. & Berman, O. L. Phase transitions in a system of spatially separated electrons and holes. JETP 84, 1027–1035 (1997).

    Article  ADS  Google Scholar 

  20. Ben-Tabou de-Leon, S. & Laikhtman, B. Exciton-exciton interactions in quantum wells: optical properties and energy and spin relaxation. Phys. Rev. B 63, 125306 (2001).

    Article  ADS  Google Scholar 

  21. Keldysh, L. V. The electron–hole liquid in semiconductors. Contemp. Phys. 27, 395–428 (1986).

    Article  ADS  Google Scholar 

  22. Zrenner, A. et al. Indirect excitons in coupled quantum well structures. Surf. Sci. 263, 496–501 (1992).

    Article  ADS  Google Scholar 

  23. Vörös, Z., Balili, R., Snoke, D. W., Pfeiffer, L. & West, K. Long-distance diffusion of excitons in double quantum well structures. Phys. Rev. Lett. 94, 226401 (2005).

    Article  ADS  Google Scholar 

  24. Gärtner, A., Holleitner, A. W., Kotthaus, J. P. & Schuh, D. Drift mobility of long-living excitons in coupled GaAs quantum wells. Appl. Phys. Lett. 89, 052108 (2006).

    Article  ADS  Google Scholar 

  25. Fogler, M. M., Yang, S., Hammack, A. T., Butov, L. V. & Gossard, A. C. Effect of spatial resolution on the estimates of the coherence length of excitons in quantum wells. Phys. Rev. B 78, 035411 (2008).

    Article  ADS  Google Scholar 

  26. High, A. A. et al. Spontaneous coherence in a cold exciton gas. Nature 483, 584–588 (2012).

    Article  ADS  Google Scholar 

  27. Alloing, M. et al. Evidence for a Bose–Einstein condensate of excitons. Europhys. Lett. 107, 10012 (2014).

    Article  ADS  Google Scholar 

  28. Stern, M., Umansky, V. & Bar-Joseph, I. Exciton liquid in coupled quantum wells. Science 343, 55–57 (2014).

    Article  ADS  Google Scholar 

  29. Lazić, S. et al. Scalable interconnections for remote indirect exciton systems based on acoustic transport. Phys. Rev. B 89, 085313 (2014).

    Article  ADS  Google Scholar 

  30. Fedichkin, F. et al. Transport of dipolar excitons in (Al,Ga)N/GaN quantum wells. Phys. Rev. B 91, 205424 (2015).

    Article  ADS  Google Scholar 

  31. Cohen, K. et al. Dipolar liquid of excitons. Nano Lett. 16, 3726–3731 (2016).

    Article  ADS  Google Scholar 

  32. Gorbunov, A. V. & Timofeev, V. B. Coherence of Bose–Einstein condensates of dipolar excitons in GaAs/AlGaAs heterostructures. Low. Temp. Phys. 42, 340–346 (2016).

    Article  ADS  Google Scholar 

  33. Leonard, J. R. et al. Moiré pattern of interference dislocations in condensate of indirect excitons. Nat. Commun. 12, 1175 (2021).

    Article  ADS  Google Scholar 

  34. Sivalertporn, K., Mouchliadis, L., Ivanov, A. L., Philp, R. & Muljarov, E. A. Direct and indirect excitons in semiconductor coupled quantum wells in an applied electric field. Phys. Rev. B 85, 045207 (2012).

    Article  ADS  Google Scholar 

  35. Comte, C. & Noziéres, P. Exciton Bose condensation: the ground state of an electron–hole gas – I. Mean field description of a simplified model. J. de Phys. 43, 1069–1081 (1982).

    Article  Google Scholar 

  36. Choksy, D. J. et al. Attractive and repulsive dipolar interaction in bilayers of indirect excitons. Phys. Rev. B 103, 045126 (2021).

    Article  ADS  Google Scholar 

  37. De Palo, S., Rapisarda, F. & Senatore, G. Excitonic condensation in a symmetric electron–hole bilayer. Phys. Rev. Lett. 88, 206401 (2002).

    Article  ADS  Google Scholar 

  38. Schleede, J., Filinov, A., Bonitz, M. & Fehske, H. Phase diagram of bilayer electron–hole plasmas. Contrib. Plasma Phys. 52, 819–826 (2012).

    Article  ADS  Google Scholar 

  39. Maezono, R., Ríos, P. L., Ogawa, T. & Needs, R. J. Excitons and biexcitons in symmetric electron–hole bilayers. Phys. Rev. Lett. 110, 216407 (2013).

    Article  ADS  Google Scholar 

  40. Fogler, M. M., Butov, L. V. & Novoselov, K. S. High-temperature superfluidity with indirect excitons in van der Waals heterostructures. Nat. Commun. 5, 4555 (2014).

    Article  ADS  Google Scholar 

  41. Dignam, M. M. & Sipe, J. E. Exciton states in coupled double quantum wells in a static electric field. Phys. Rev. B 43, 4084–4096 (1991).

    Article  ADS  Google Scholar 

  42. Skocpol, W. J. & Tinkham, M. Fluctuations near superconducting phase transitions. Rep. Prog. Phys. 38, 1049–1097 (1975).

  43. Aslamazov, L. G. & Larkin, A. I. Effect of fluctuations on properties of a superconductor above critical temperature. Sov. Phys. Solid State 10, 875–880 (1968).

    Google Scholar 

  44. Schmitt-Rink, S., Ell, C. & Haug, H. Many-body effects in the absorption, gain, and luminescence spectra of semiconductor quantum-well structures. Phys. Rev. B 33, 1183–1189 (1986).

    Article  ADS  Google Scholar 

  45. Des Cloizeaux, J. Exciton instability and crystallographic anomalies in semiconductors. J. Phys. Chem. Solids 26, 259–266 (1965).

    Article  Google Scholar 

  46. Kozlov, A. N. & Maksimov, L. A. The metal–dielectric divalent crystal phase transition. Sov. Phys. JETP 21, 790–795 (1965).

    ADS  Google Scholar 

  47. Jerome, D., Rice, T. M. & Kohn, W. Excitonic insulator. Phys. Rev. 158, 462–475 (1967).

  48. Halperin, B. I. & Rice, T. M. The excitonic state at the semiconductor–semimetal transition. Solid State Phys. 21, 115–192 (1968).

    Article  Google Scholar 

  49. Eisenstein, J. P. & MacDonald, A. H. Bose–Einstein condensation of excitons in bilayer electron systems. Nature 432, 691–694 (2004).

    Article  ADS  Google Scholar 

  50. Rontani, M. & Sham, L. J. Coherent transport in a homojunction between an excitonic insulator and semimetal. Phys. Rev. Lett. 94, 186404 (2005).

    Article  ADS  Google Scholar 

  51. Du, L. et al. Evidence for a topological excitonic insulator in InAs/GaSb bilayers. Nat. Commun. 8, 1971 (2017).

    Article  ADS  Google Scholar 

  52. Kogar, A. et al. Signatures of exciton condensation in a transition metal dichalcogenide. Science 358, 1314–1317 (2017).

  53. Liu, X., Watanabe, K., Taniguchi, T., Halperin, B. I. & Kim, P. Quantum Hall drag of exciton condensate in graphene. Nat. Phys. 13, 746–750 (2017).

    Article  Google Scholar 

  54. Li, J. I. A., Taniguchi, T., Watanabe, K., Hone, J. & Dean, C. R. Excitonic superfluid phase in double bilayer graphene. Nat. Phys. 13, 751–755 (2017).

    Article  Google Scholar 

  55. Burg, G. W. et al. Strongly enhanced tunneling at total charge neutrality in double-bilayer graphene-WSe2 heterostructures. Phys. Rev. Lett. 120, 177702 (2018).

    Article  ADS  Google Scholar 

  56. Sun, Z., Kaneko, T., Golež, D. & Millis, A. J. Second-order Josephson effect in excitonic insulators. Phys. Rev. Lett. 127, 127702 (2021).

    Article  ADS  Google Scholar 

  57. Ataei, S. S., Varsano, D., Molinari, E. & Rontani, M. Evidence of ideal excitonic insulator in bulk MoS2 under pressure. Proc. Natl Acad. Sci. USA 118, e2010110118 (2021).

    Article  Google Scholar 

  58. Kim, K. et al. Direct observation of excitonic instability in Ta2NiSe5. Nat. Commun. 12, 1969 (2021).

    Article  ADS  Google Scholar 

  59. Liu, X. et al. Crossover between strongly coupled and weakly coupled exciton superfluids. Science 375, 205–209 (2022).

    Article  ADS  Google Scholar 

  60. Jia, Y. et al. Evidence for a monolayer excitonic insulator. Nat. Phys. 18, 87–93 (2022).

    Article  Google Scholar 

  61. Sun, B. et al. Evidence for equilibrium exciton condensation in monolayer WTe2. Nat. Phys. 18, 94–99 (2022).

  62. Gu, J. et al. Dipolar excitonic insulator in a moiré lattice. Nat. Phys. 18, 395–400 (2022).

    Article  Google Scholar 

  63. Zhang, Z. et al. Correlated interlayer exciton insulator in heterostructures of monolayer WSe2 and moiré WS2/WSe2. Nat. Phys. https://doi.org/10.1038/s41567-022-01702-z (2022).

  64. Chen, D. et al. Excitonic insulator in a heterojunction moiré superlattice. Nat. Phys. https://doi.org/10.1038/s41567-022-01703-y (2022).

  65. Zwierlein, M. W., Abo-Shaeer, J. R., Schirotzek, A., Schunck, C. H. & Ketterle, W. Vortices and superfluidity in a strongly interacting Fermi gas. Nature 435, 1047–1051 (2005).

    Article  ADS  Google Scholar 

  66. Choksy, D. J., Szwed, E. A., Butov, L. V., Baldwin, K. W. & Pfeiffer, L. N. Data for Fermi edge singularity in neutral electron–hole system paper. Figshare https://figshare.com/s/513eebd7af01900af912 (2023).

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Acknowledgements

We thank M. Fogler, L. Fowler-Gerace, J. Leonard, L. Sham and B. Vermilyea for discussions. The spectroscopy studies were supported by NSF grant no. 1905478 (L.V.B.). The coherence studies were supported by DOE Office of Basic Energy Sciences under award no. DE-FG02-07ER46449 (L.V.B.). The heterostructure growth was funded by the Gordon and Betty Moore Foundation’s EPiQS Initiative, grant GBMF9615 to L.N.P., and by National Science Foundation MRSEC grant DMR 2011750 to Princeton University.

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  1. These authors contributed equally: D. J. Choksy, E. A. Szwed.

Authors and Affiliations

  1. Department of Physics, University of California at San Diego, La Jolla, CA, USA

    D. J. Choksy, E. A. Szwed & L. V. Butov

  2. Princeton University, Princeton, NJ, USA

    K. W. Baldwin & L. N. Pfeiffer

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Contributions

L.V.B. designed the project. K.W.B. and L.N.P. grew the GaAs heterostructures. D.J.C. and E.A.S. performed the measurements. D.J.C., E.A.S. and L.V.B. analysed the data. L.V.B. wrote the manuscript with inputs from all the authors.

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Correspondence to L. V. Butov.

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Choksy, D.J., Szwed, E.A., Butov, L.V. et al. Fermi edge singularity in neutral electron–hole system. Nat. Phys. 19, 1275–1279 (2023). https://doi.org/10.1038/s41567-023-02096-2

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