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Terahertz parametric amplification as a reporter of exciton condensate dynamics

Nature Materials volume 23, pages 796–802 (2024)Cite this article

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Abstract

Condensates are a hallmark of emergence in quantum materials such as superconductors and charge density waves. Excitonic insulators are an intriguing addition to this library, exhibiting spontaneous condensation of electron–hole pairs. However, condensate observables can be obscured through parasitic coupling to the lattice. Here we employ nonlinear terahertz spectroscopy to disentangle such obscurants through measurement of the quantum dynamics. We target Ta2NiSe5, a putative room-temperature excitonic insulator in which electron–lattice coupling dominates the structural transition (Tc = 326 K), hindering identification of excitonic correlations. A pronounced increase in the terahertz reflectivity manifests following photoexcitation and exhibits a Bose–Einstein condensation-like temperature dependence well below the Tc, suggesting an approach to monitor the exciton condensate dynamics. Nonetheless, dynamic condensate–phonon coupling remains as evidenced by peaks in the enhanced reflectivity spectrum at select infrared-active phonon frequencies, indicating that parametric reflectivity enhancement arises from phonon squeezing. Our results highlight that coherent dynamics can drive parametric stimulated emission.

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Fig. 1: Experimental study of TNS.
Fig. 2: Temperature dependence of the reflectivity enhancement.
Fig. 3: Reflectivity enhancement dynamics.
Fig. 4: Description of parametric amplification at 4.7 THz.

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Data availability

The data presented in this manuscript are available from the corresponding author upon reasonable request. Source data are provided with this paper.

Code availability

The data presented in this manuscript were analysed and plotted with MATLAB v.R2018a and are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank D. Hsieh, P. Narang, M. K. Liu and A. Kogar for fruitful discussions. S.R.U.H., M.H.M., J. Zhu, Y.Z., J.P.W., G.-F.Z., J. Zhang, J.G.C., E.D. and R.D.A. acknowledge support from the DARPA ‘Driven Nonequilibrium Quantum Systems’ (DRINQS) programme under award number D18AC00014. E.D. acknowledges support from SNSF project 200021_212899 and ARO grant number W911NF-21-1-0184. L.W., S.L. and A.R. acknowledge support from the European Research Council (ERC-2015-AdG694097), the Cluster of Excellence ‘Advanced Imaging of Matter’ (AIM), Grupos Consolidados (IT1249-19) and Deutsche Forschungsgemeinschaft (DFG) – SFB-925 – project 170620586. A.R. also thanks the Flatiron Institute, a division of the Simons Foundation.

Author information

Author notes

  1. Sheikh Rubaiat Ul Haque

    Present address: Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

Authors and Affiliations

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

    Sheikh Rubaiat Ul Haque, Yuan Zhang, Gu-Feng Zhang, Jingdi Zhang & Richard D. Averitt

  2. Department of Physics, Harvard University, Cambridge, MA, USA

    Marios H. Michael & Eugene Demler

  3. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Junbo Zhu, Joshua P. Wakefield & Joseph G. Checkelsky

  4. Max Planck Institute for the Structure and Dynamics of Matter (MPSD), Hamburg, Germany

    Lukas Windgätter, Simone Latini & Angel Rubio

  5. Department of Physics, The Hong Kong University of Science and Technology, Hongkong, China

    Jingdi Zhang

  6. Center for Computational Quantum Physics, The Flatiron Institute, New York, NY, USA

    Angel Rubio

  7. Institute for Theoretical Physics, ETH Zürich, Zürich, Switzerland

    Eugene Demler

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Contributions

R.D.A. and S.R.U.H. conceived the project. J. Zhu, J.P.W. and J.G.C. performed the material growth and characterization. S.R.U.H., G.-F.Z. and J. Zhang built the experimental set-up. S.R.U.H., Y.Z. and G.-F.Z. performed the optical pump–THz probe measurements. S.R.U.H. analysed the data. M.H.M. and E.D. performed the first-principles calculation and numerical simulations. L.W., S.L. and A.R. performed the DFT analysis. All authors participated in the discussion and interpretations of the results. R.D.A. and E.D. supervised the project. S.R.U.H. and R.D.A. wrote the manuscript with input from all authors.

Corresponding author

Correspondence to Richard D. Averitt.

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Extended data

Extended Data Fig. 1 Transport properties of Ta2 NiSe5.

Resistivity of Ta2 NiSe5 single crystal plotted against the temperature. The blue triangle emphasizes an anomaly at T=326 K, corresponding to the temperature of the phase transition.

Source data

Extended Data Fig. 2 Experimental set-up and THz generation.

a, Experimental set-up for near-infrared pump – broadband THz probe spectroscopy. DWP: dual wave plate, OPA: optical parametric amplifier, BBO: β-Barium Borate, QWP: quarter wave plate, PD: photodiode. 2.4 μm pump beams are generated as idler beams from the OPA while broadband THz probe pulses are generated from a two-colour laser-induced air plasma. GaP crystal is utilized as the EO sampling crystal. b, Horizontally polarized 800 nm pulses generate vertically polarized 400 nm pulses after passing through the BBO crystal. The DWP rotates the 800 nm polarization from horizontal to vertical. Both beams are focused into the air and create an air plasma which radiates broadband THz waves. Arrows indicate the polarization directions. Inset shows a detailed schematic of the THz generation process from the air plasma.

Extended Data Fig. 3 Time-domain THz signal and corresponding spectrum.

a, Reflected time-domain signal (TDS) from a gold mirror (reference), a 300 μm-thick 〈110〉 GaP was used to detect the signal. b, The corresponding normalized spectrum showing a broadband spectral regime of 0.5–7.5 THz.

Source data

Extended Data Fig. 4 Equilibrium reflectivity and optical conductivity.

a, Equilibrium reflectivity and b, optical conductivity along the a-axis as a function of temperature. Phonon locations are denoted by grey dashed lines.

Source data

Extended Data Fig. 5 Dynamics of the reflectivity enhancement.

Dynamics of reflectivity enhancement ΔR/R at 4.7 THz (left axes, closed squares) and integrated pump-induced change in reflectivity spectral weight Δη (right axes, open circles) as a function of fluences of 0.2 mJ cm−2 (a,c,e,g,i,k,m,o) and 0.4 mJ cm−2 (b,d,f,h,j,l,n,p) at 90 K (a,b), 120 K (c,d), 150 K (e,f), 180 K (g,h), 210 K (i,j), 240 (k,l), 270 K(m,n), and 295 K (o,p). Both sets of data were plotted on the same scale for comparison. The dotted lines represent single exponential decay function utilized to determine the relaxation time T. All error bars represent the standard errors of the mean from two independent measurements.

Source data

Extended Data Fig. 6 Specific heat analysis.

a, Specific heat of TNS obtained from Ref. 8, then modelled with a Debye fitting. b, Fluence-dependent temperature increase ΔT for different initial temperatures Ti. It is observed from the plot that the photoinduced temperature rise is minimal, ruling out a thermal origin of the signal.

Source data

Extended Data Fig. 7 DFT calculation.

Recalculated band structures in the monoclinic phase after displacement of the IR-phonon coordinate along the positive (red dashed line) and negative (dark blue dashed line) directions with respect to the equilibrium structure (black solid line) for a, mode 21, b, mode 22, c, mode 25 and d, mode 26 using the PBE functional. Green ellipses represent the shift in bands. Phonon mode 26 shows the largest renormalization and thus the strongest coupling to the band structure upon displacement along its eigenmode. Insets show the zoomed in profiles of the renormalized band structures. Blue arrows signify the direction of the energy shift.

Extended Data Fig. 8 Evolution of the 4.69 THz mode.

The temperature-dependence of the electron–phonon coupling for 4.69 THz Bu mode and (mode 26) in the a, monoclinic and b, orthorhombic phases using the PBE functional. For the monoclinic phase, the electron–phonon coupling is strong and thus the shift in the bands owing to the displacement of the phonon coordinate along its eigenmode is large. Contrary to this, the band shift almost disappears for the orthorhombic phase. This demonstrates that the electron–phonon coupling is mediated by the low-temperature order parameter.

Extended Data Table 1 IR-active phonon modes near 4.5 THz
Full size table

Supplementary information

Supplementary Information

Suppmentary Figs, 1–18, refs. 58–60 and sections on phonon squeezing in detail, telation between phonon squeezing and reflectivity enhancement, penetration depth mismatch analysis, thermal effect analysis, possibility of thermal phonon shift as an alternative interpretation, and oossibility of THz emission.

Reporting Summary

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Haque, S.R.U., Michael, M.H., Zhu, J. et al. Terahertz parametric amplification as a reporter of exciton condensate dynamics. Nat. Mater. 23, 796–802 (2024). https://doi.org/10.1038/s41563-023-01755-2

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