Skip to main content

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.

A Hubbard exciton fluid in a photo-doped antiferromagnetic Mott insulator

Nature Physics (2023)Cite this article

Subjects

Abstract

The undoped antiferromagnetic Mott insulator naturally has one charge carrier per lattice site. When it is doped with additional carriers, they are unstable to spin-fluctuation-mediated Cooper pairing as well as other unconventional types of charge, spin and orbital current ordering. Photo-excitation can produce charge carriers in the form of empty (holons) and doubly occupied (doublons) sites that may also exhibit charge instabilities. There is evidence that antiferromagnetic correlations enhance attractive interactions between holons and doublons, which can then form bound pairs known as Hubbard excitons, and that these might self-organize into an insulating Hubbard exciton fluid. However, this out-of-equilibrium phenomenon has not been experimentally detected. Here we report the transient formation of a Hubbard exciton fluid in the antiferromagnetic Mott insulator Sr2IrO4 using ultrafast terahertz conductivity. Following photo-excitation, we observe rapid spectral-weight transfer from a Drude metallic response to an insulating response. The latter is characterized by a finite-energy peak originating from intraexcitonic transitions, whose assignment is corroborated by our numerical simulations of an extended Hubbard model. The lifetime of the peak is short (approximately one picosecond) and scales exponentially with the Mott gap size, implying extremely strong coupling to magnon modes.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Electrodynamic properties of Sr2IrO4.
Fig. 2: Photo-doping-induced optical conductivity transients of Sr2IrO4.
Fig. 3: Temperature dependence of HE decay.
Fig. 4: HE spectrum and characteristics obtained from effective model numerics.

Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. Regan, E. C. et al. Emerging exciton physics in transition metal dichalcogenide heterobilayers. Nat. Rev. Mater. 7, 778–795 (2022).

    Article  ADS  Google Scholar 

  2. Tartakovskii, A. Excitons in 2D heterostructures. Nat. Rev. Phys. 2, 8–9 (2020).

    Article  Google Scholar 

  3. Dimitriev, O. P. Dynamics of excitons in conjugated molecules and organic semiconductor systems. Chem. Rev. 122, 8487–8593 (2022).

    Article  Google Scholar 

  4. Bae, S. & Sim, S. Anisotropic excitons in 2D rhenium dichalcogenides: a mini-review. J. Korean Phys. Soc. 81, 532–548 (2022).

    Article  ADS  Google Scholar 

  5. Baranowski, M. & Plochocka, P. Excitons in metal-halide perovskites. Adv. Energy Mater. 10, 1903659 (2020).

    Article  Google Scholar 

  6. Miller, R. C. & Kleinman, D. A. Excitons in GaAs quantum wells. J. Lumin. 30, 520–540 (1985).

    Article  Google Scholar 

  7. Bardeen, C. J. The structure and dynamics of molecular excitons. Annu. Rev. Phys. Chem. 65, 127–148 (2014).

    Article  ADS  Google Scholar 

  8. Kazimierczuk, T., Fröhlich, D., Scheel, S., Stolz, H. & Bayer, M. Giant Rydberg excitons in the copper oxide Cu2O. Nature 514, 343–347 (2014).

    Article  ADS  Google Scholar 

  9. Jadczak, J. et al. Exciton binding energy and hydrogenic Rydberg series in layered ReS2. Sci. Rep. 9, 1578 (2019).

    Article  ADS  Google Scholar 

  10. Chernikov, A. et al. Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2. Phys. Rev. Lett. 113, 076802 (2014).

    Article  ADS  Google Scholar 

  11. Ye, Z. et al. Probing excitonic dark states in single-layer tungsten disulphide. Nature 513, 214–218 (2014).

    Article  ADS  Google Scholar 

  12. Mak, K. F. & Shan, J. Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides. Nat. Photon. 10, 216–226 (2016).

    Article  ADS  Google Scholar 

  13. Snoke, D. Spontaneous Bose coherence of excitons and polaritons. Science 298, 1368–1372 (2002).

    Article  ADS  Google Scholar 

  14. Kaindl, R. A., Carnahan, M. A., Hägele, D., Lövenich, R. & Chemla, D. S. Ultrafast terahertz probes of transient conducting and insulating phases in an electron–hole gas. Nature 423, 734–738 (2003).

    Article  ADS  Google Scholar 

  15. Zhang, Q. et al. Stability of high-density two-dimensional excitons against a Mott transition in high magnetic fields probed by coherent terahertz spectroscopy. Phys. Rev. Lett. 117, 207402 (2016).

    Article  ADS  Google Scholar 

  16. Butov, L. V., Gossard, A. C. & Chemla, D. S. Macroscopically ordered state in an exciton system. Nature 418, 751–754 (2002).

    Article  ADS  Google Scholar 

  17. à la Guillaume, C. B. Electron-hole droplets in semiconductors. in Collective Excitations in Solids (ed Di Bartolo, B.) 633–642 (Springer, 1983).

  18. Gnatchenko, S. L., Kachur, I. S., Piryatinskaya, V. G., Vysochanskii, Y. M. & Gurzan, M. I. Exciton-magnon structure of the optical absorption spectrum of antiferromagnetic MnPS3. Low Temp. Phys. 37, 144–148 (2011).

    Article  ADS  Google Scholar 

  19. Meltzer, R. S., Chen, M. Y., McClure, D. S. & Lowe-Pariseau, M. Exciton-magnon bound state in MnF2 and the exciton dispersion in MnF2 and RbMnF3. Phys. Rev. Lett. 21, 913–916 (1968).

    Article  ADS  Google Scholar 

  20. Bae, Y. J. et al. Exciton-coupled coherent magnons in a 2D semiconductor. Nature 609, 282–286 (2022).

    Article  ADS  Google Scholar 

  21. Kang, S. et al. Coherent many-body exciton in van der Waals antiferromagnet NiPS3. Nature 583, 785–789 (2020).

    Article  ADS  Google Scholar 

  22. Lenarčič, Z. & Prelovšek, P. Charge recombination in undoped cuprates. Phys. Rev. B 90, 235136 (2014).

    Article  ADS  Google Scholar 

  23. Lenarčič, Z. & Prelovšek, P. Ultrafast charge recombination in a photoexcited Mott-Hubbard insulator. Phys. Rev. Lett. 111, 016401 (2013).

    Article  ADS  Google Scholar 

  24. Huang, T.-S., Baldwin, C. L., Hafezi, M. & Galitski, V. Spin-mediated Mott excitons. Phys. Rev. B 107, 075111 (2023).

    Article  ADS  Google Scholar 

  25. Shinjo, K., Tamaki, Y., Sota, S. & Tohyama, T. Density-matrix renormalization group study of optical conductivity of the Mott insulator for two-dimensional clusters. Phys. Rev. B 104, 205123 (2021).

    Article  ADS  Google Scholar 

  26. Wróbel, P. & Eder, R. Excitons in Mott insulators. Phys. Rev. B 66, 035111 (2002).

    Article  ADS  Google Scholar 

  27. Clarke, D. G. Particle-hole bound states in Mott-Hubbard insulators. Phys. Rev. B 48, 7520–7525 (1993).

    Article  ADS  Google Scholar 

  28. Grusdt, F., Demler, E. & Bohrdt, A. Pairing of holes by confining strings in antiferromagnets. SciPost Phys. 14, 090 (2023).

    Article  ADS  MathSciNet  Google Scholar 

  29. Tohyama, T., Inoue, Y., Tsutsui, K. & Maekawa, S. Exact diagonalization study of optical conductivity in the two-dimensional Hubbard model. Phys. Rev. B 72, 045113 (2005).

    Article  ADS  Google Scholar 

  30. Stephan, W. & Penc, K. Dynamical density-density correlations in one-dimensional Mott insulators. Phys. Rev. B 54, R17269–R17272 (1996).

    Article  ADS  Google Scholar 

  31. Essler, F. H. L., Gebhard, F. & Jeckelmann, E. Excitons in one-dimensional Mott insulators. Phys. Rev. B 64, 125119 (2001).

    Article  ADS  Google Scholar 

  32. Wall, S. et al. Quantum interference between charge excitation paths in a solid-state Mott insulator. Nat. Phys. 7, 114–118 (2011).

    Article  Google Scholar 

  33. Miyamoto, T. et al. Biexciton in one-dimensional Mott insulators. Commun. Phys. 2, 131 (2019).

    Article  Google Scholar 

  34. Miller, R. & Kleinman, D. Excitons in GaAs quantum wells. J. Lumin. 30, 520–540 (1985).

    Article  Google Scholar 

  35. Terashige, T. et al. Doublon-holon pairing mechanism via exchange interaction in two-dimensional cuprate Mott insulators. Sci. Adv. 5, eaav2187 (2019).

    Article  ADS  Google Scholar 

  36. Gretarsson, H. et al. Crystal-field splitting and correlation effect on the electronic structure of A2IrO3. Phys. Rev. Lett. 110, 076402 (2013).

    Article  ADS  Google Scholar 

  37. Wang, Y. Y. et al. Momentum-dependent charge transfer excitations in Sr2CuO2Cl2 angle-resolved electron energy loss spectroscopy. Phys. Rev. Lett. 77, 1809–1812 (1996).

    Article  ADS  Google Scholar 

  38. Gössling, A. et al. Mott-Hubbard exciton in the optical conductivity of YTiO3 and SmTiO3. Phys. Rev. B 78, 075122 (2008).

    Article  ADS  Google Scholar 

  39. Alpichshev, Z., Mahmood, F., Cao, G. & Gedik, N. Confinement-deconfinement transition as an indication of spin-liquid-type behavior in Na2IrO3. Phys. Rev. Lett. 114, 017203 (2015).

    Article  ADS  Google Scholar 

  40. Novelli, F. et al. Ultrafast optical spectroscopy of the lowest energy excitations in the Mott insulator compound YVO3: evidence for Hubbard-type excitons. Phys. Rev. B 86, 165135 (2012).

    Article  ADS  Google Scholar 

  41. Lovinger, D. J. et al. Influence of spin and orbital fluctuations on Mott-Hubbard exciton dynamics in LaVO3 thin films. Phys. Rev. B 102, 115143 (2020).

    Article  ADS  Google Scholar 

  42. Okamoto, H. et al. Photoinduced transition from Mott insulator to metal in the undoped cuprates Nd2CuO4 and La2CuO4. Phys. Rev. B 83, 125102 (2011).

    Article  ADS  Google Scholar 

  43. Kim, B. J. et al. Novel Jeff = 1/2 Mott state induced by relativistic spin-orbit coupling in Sr2IrO4. Phys. Rev. Lett. 101, 076402 (2008).

    Article  ADS  Google Scholar 

  44. Moon, S. J. et al. Temperature dependence of the electronic structure of the Jeff = 1/2 Mott insulator Sr2IrO4 studied by optical spectroscopy. Phys. Rev. B 80, 195110 (2009).

    Article  ADS  Google Scholar 

  45. Seo, J. H. et al. Infrared probe of pseudogap in electron-doped Sr2IrO4. Sci. Rep. 7, 10494 (2017).

    Article  ADS  Google Scholar 

  46. Kim, J. et al. Magnetic excitation spectra of Sr2IrO4 probed by resonant inelastic X-ray scattering: establishing links to cuprate superconductors. Phys. Rev. Lett. 108, 177003 (2012).

    Article  ADS  Google Scholar 

  47. Cao, G., Bolivar, J., McCall, S., Crow, J. E. & Guertin, R. P. Weak ferromagnetism, metal-to-nonmetal transition, and negative differential resistivity in single-crystal Sr2IrO4. Phys. Rev. B 57, R11039–R11042 (1998).

    Article  ADS  Google Scholar 

  48. Dashwood, C. D. et al. Momentum-resolved lattice dynamics of parent and electron-doped Sr2IrO4. Phys. Rev. B 100, 085131 (2019).

    Article  ADS  Google Scholar 

  49. Dean, M. P. M. et al. Ultrafast energy- and momentum-resolved dynamics of magnetic correlations in the photo-doped Mott insulator Sr2IrO4. Nat. Mater. 15, 601–605 (2016).

    Article  ADS  Google Scholar 

  50. Bahr, S. et al. Low-energy magnetic excitations in the spin-orbital Mott insulator Sr2IrO4. Phys. Rev. B 89, 180401 (2014).

    Article  ADS  Google Scholar 

  51. Steinleitner, P. et al. Direct observation of ultrafast exciton formation in a monolayer of WSe2. Nano Lett. 17, 1455–1460 (2017).

    Article  ADS  Google Scholar 

  52. Kaindl, R. A., Hägele, D., Carnahan, M. A. & Chemla, D. S. Transient terahertz spectroscopy of excitons and unbound carriers in quasi-two-dimensional electron-hole gases. Phys. Rev. B 79, 045320 (2009).

    Article  ADS  Google Scholar 

  53. Hsieh, D., Mahmood, F., Torchinsky, D. H., Cao, G. & Gedik, N. Observation of a metal-to-insulator transition with both Mott-Hubbard and Slater characteristics in Sr2IrO4 from time-resolved photocarrier dynamics. Phys. Rev. B 86, 035128 (2012).

    Article  ADS  Google Scholar 

  54. Piovera, C. et al. Time-resolved photoemission of Sr2IrO4. Phys. Rev. B 93, 241114 (2016).

    Article  ADS  Google Scholar 

  55. Xu, B. et al. Optical signature of a crossover from Mott- to Slater-type gap in Sr2IrO4. Phys. Rev. Lett. 124, 027402 (2020).

    Article  ADS  Google Scholar 

  56. Poellmann, C. et al. Resonant internal quantum transitions and femtosecond radiative decay of excitons in monolayer WSe2. Nat. Mater. 14, 889–893 (2015).

    Article  ADS  Google Scholar 

  57. Hu, Y. et al. Spectroscopic evidence for electron-boson coupling in electron-doped Sr2IrO4. Phys. Rev. Lett. 123, 216402 (2019).

    Article  ADS  Google Scholar 

  58. Li, Y. et al. Strong lattice correlation of non-equilibrium quasiparticles in a pseudospin-1/2 Mott insulator Sr2IrO4. Sci. Rep. 6, 19302 (2016).

    Article  ADS  Google Scholar 

  59. Lenarčič, Z., Eckstein, M. & Prelovšek, P. Exciton recombination in one-dimensional organic Mott insulators. Phys. Rev. B 92, 201104 (2015).

    Article  ADS  Google Scholar 

  60. Strohmaier, N. et al. Observation of elastic doublon decay in the Fermi-Hubbard model. Phys. Rev. Lett. 104, 080401 (2010).

    Article  ADS  Google Scholar 

  61. Gretarsson, H. et al. Two-magnon Raman scattering and pseudospin-lattice interactions in Sr2IrO4 and Sr3Ir2O7. Phys. Rev. Lett. 116, 136401 (2016).

    Article  ADS  Google Scholar 

  62. Gretarsson, H. et al. Persistent paramagnons deep in the metallic phase of Sr2−xLaxIrO4. Phys. Rev. Lett. 117, 107001 (2016).

    Article  ADS  Google Scholar 

  63. Fujiyama, S. et al. Two-dimensional Heisenberg behavior of Jeff = 1/2 isospins in the paramagnetic state of the spin-orbital Mott insulator Sr2IrO4. Phys. Rev. Lett. 108, 247212 (2012).

    Article  ADS  Google Scholar 

  64. Watanabe, H., Shirakawa, T. & Yunoki, S. Microscopic study of a spin-orbit-induced Mott insulator in Ir oxides. Phys. Rev. Lett. 105, 216410 (2010).

    Article  ADS  Google Scholar 

  65. Wang, F. & Senthil, T. Twisted Hubbard model for Sr2IrO4: magnetism and possible high temperature superconductivity. Phys. Rev. Lett. 106, 136402 (2011).

    Article  ADS  Google Scholar 

  66. Tohyama, T. Symmetry of photoexcited states and large-shift Raman scattering in two-dimensional Mott insulators. J. Phys. Soc. Jpn 75, 034713 (2006).

    Article  ADS  Google Scholar 

  67. Mentink, J. H., Balzer, K. & Eckstein, M. Ultrafast and reversible control of the exchange interaction in Mott insulators. Nat. Commun. 6, 6708 (2015).

    Article  ADS  Google Scholar 

  68. Hunt, C. R. Manipulating Superconductivity in Cuprates with Selective Ultrafast Excitation. PhD thesis, Univ. Illinois at Urbana-Champaign (2015).

  69. Bhandari, C., Popović, Z. S. & Satpathy, S. Electronic structure and optical properties of Sr2IrO4 under epitaxial strain. New J. Phys. 21, 013036 (2019).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank L. Balents, M. Ye, R. D. Averitt, P. A. Lee, M. Mitrano, M. Buzzi, S. K. Cushing, P. Prelovšek, D. Golež and V. Galitski for useful discussions. We thank S. J. Moon for sharing his equilibrium optical conductivity results. This work is supported by ARO MURI grant no. W911NF-16-1-0361. D.H. acknowledges support for instrumentation from the David and Lucile Packard Foundation and from the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (PHY-1733907). S.D.W. acknowledges partial support via NSF award DMR-1729489. X.L. acknowledges support from the Caltech Postdoctoral Prize Fellowship and IQIM. M.B. acknowledges support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1-390534769. Z.L. was funded by the Gordon and Betty Moore Foundation’s EPiQS initiative, grant no. GBMF4545, and J1-2463 project and P1-0044 program of the Slovenian Research Agency.

Author information

Author notes

  1. These authors contributed equally: Omar Mehio, Xinwei Li, Honglie Ning.

Authors and Affiliations

  1. Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA

    Omar Mehio, Xinwei Li, Honglie Ning, Yuchen Han, Nicholas J. Laurita & David Hsieh

  2. Department of Physics, California Institute of Technology, Pasadena, CA, USA

    Omar Mehio, Xinwei Li, Honglie Ning, Yuchen Han, Nicholas J. Laurita & David Hsieh

  3. Department for Theoretical Physics, Jozef Stefan Institute, Ljubljana, Slovenia

    Zala Lenarčič

  4. Department of Physics, University of California, Berkeley, CA, USA

    Zala Lenarčič

  5. Institute for Theoretical Physics, University of Cologne, Cologne, Germany

    Michael Buchhold

  6. Materials Department, University of California, Santa Barbara, CA, USA

    Zach Porter & Stephen D. Wilson

Authors
  1. Omar Mehio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xinwei Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Honglie Ning
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zala Lenarčič
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yuchen Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Michael Buchhold
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Zach Porter
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Nicholas J. Laurita
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Stephen D. Wilson
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. David Hsieh
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

O.M. and D.H. conceived the experiment. O.M. constructed the time-resolved time-domain THz spectrometer with contributions from X.L. and N.J.L. O.M., X.L., H.N. and Y.H. collected and analysed the data. Z.L. performed the exact diagonalization calculations and interpreted the results with O.M. and M.B. Z.P. and S.W. synthesized and characterized the sample. O.M. and D.H. wrote the paper with input from all authors.

Corresponding author

Correspondence to David Hsieh.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks Edoardo Baldini and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

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

Extended data

Extended Data Fig. 1 Drude-Lorentz fitting of a typical tr-TDTS spectrum of Sr2IrO4.

a,b Individual components of the Drude-Lorentz fitting of Δσ1(ω) (a) and Δσ2(ω) (b) plotted with the original data at t = 1.5 ps. The pump energy was fixed at 0.6 eV, resonant with the α transition, and set to a fluence of 2 mJ/cm2. The temperature of the sample was 80 K.

Source data

Extended Data Fig. 2 Fluence independence of THz frequency decay dynamics.

a ΔE(tEOS, t) traces taken with tEOS fixed to the time where E(tEOS) is maximal (Methods) plotted as a function of the fluence of the α-resonant (0.6 eV) photo-excitation. Data was collected at a sample temperature of 80 K. b Decay constants extracted from an exponential fitting (Methods) of the traces in panel a. The solid line is a guide to the eye. Error bars are the standard deviation from the least-squares-fitting algorithm.

Source data

Extended Data Fig. 3 Temperature dependence of differential infrared reflectivity.

ΔR/R traces taken on Sr2IrO4 as a function of temperature. The probe energy was fixed at 1.55 eV. The pump energy was fixed at 0.6 eV, resonant with α, and a fluence near 2 mJ/cm2 was used. The black dashed lines are fits to a double exponential function (Methods).

Source data

Extended Data Fig. 4 Simulated dispersion of the HE states.

Eigenenergies of HtJV in the sector of a single HD pair projected onto the kx axis throughout the entire reciprocal space of the 26 site lattice. At zero center-of-mass momentum, \(\overrightarrow{k}=[0,0]\), the four lowest states are colored to indicate which excitonic states are depicted in Fig. 4 of the main text. We define 0 eV to be the energy of the lowest-energy state.

Source data

Supplementary information

Supplementary Information

Supplementary Sections I–V and Figs. 1–10.

Source data

Source Data Fig. 1

Experimental data.

Source Data Fig. 2

Experimental data.

Source Data Fig. 3

Experimental data.

Source Data Fig. 4

Theoretical simulation results.

Source Data Extended Data Fig. 1

Experimental data.

Source Data Extended Data Fig. 2

Experimental data.

Source Data Extended Data Fig. 3

Experimental data.

Source Data Extended Data Fig. 4

Theoretical simulation results.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mehio, O., Li, X., Ning, H. et al. A Hubbard exciton fluid in a photo-doped antiferromagnetic Mott insulator. Nat. Phys. (2023). https://doi.org/10.1038/s41567-023-02204-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s41567-023-02204-2

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing