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Cavity-mediated thermal control of metal-to-insulator transition in 1T-TaS2

Nature volume 622, pages 487–492 (2023)Cite this article

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Abstract

Placing quantum materials into optical cavities provides a unique platform for controlling quantum cooperative properties of matter, by both weak and strong light–matter coupling1,2. Here we report experimental evidence of reversible cavity control of a metal-to-insulator phase transition in a correlated solid-state material. We embed the charge density wave material 1T-TaS2 into cryogenic tunable terahertz cavities3 and show that a switch between conductive and insulating behaviours, associated with a large change in the sample temperature, is obtained by mechanically tuning the distance between the cavity mirrors and their alignment. The large thermal modification observed is indicative of a Purcell-like scenario in which the spectral profile of the cavity modifies the energy exchange between the material and the external electromagnetic field. Our findings provide opportunities for controlling the thermodynamics and macroscopic transport properties of quantum materials by engineering their electromagnetic environment.

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Fig. 1: Mechanisms of cavity control of quantum material states and THz characterization of 1T-TaS2 metal-to-insulator transition.
Fig. 2: Renormalization of the effective critical temperature of the metal-to-insulator phase transition within the cavity.
Fig. 3: Dependence of the effective critical temperature on the cavity geometry.
Fig. 4: Cavity-mediated thermodynamics of the metal-to-insulator phase transition in 1T-TaS2.

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Data availability

Raw hysteretic curves as a function of the cavity frequency (Fig. 4a) as well as the raw single THz scans of Figs. 3b and 4c are provided in the Supplementary Information. Further datasets collected for this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank C. Tozzo, P. van Loosdrecht, H. Hedayat and O. Abdul-Aziz for the discussions. We acknowledge P. Sutar (Jožef Stefan Institute, Ljubljana) for the growth of 1T-TaS2 crystals and discussions with J. Faist. This work was supported by the European Research Council through the project INCEPT (ERC-2015-STG, grant no. 677488). F.F. acknowledges financial support from the H2020 Marie Skłodowska-Curie actions of the European Union (grant agreement no. 799408). D.M. and P. Sutar acknowledge funding from the ARRS (grant no. P-0040). M.E. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), project ID 429529648—TRR 306 QuCoLiMa (Quantum Cooperativity of Light and Matter).

Author information

Authors and Affiliations

  1. Department of Physics, Università degli Studi di Trieste, Trieste, Italy

    Giacomo Jarc, Shahla Yasmin Mathengattil, Angela Montanaro, Francesca Giusti, Enrico Maria Rigoni & Daniele Fausti

  2. Elettra Sincrotrone Trieste, Trieste, Italy

    Giacomo Jarc, Shahla Yasmin Mathengattil, Angela Montanaro, Francesca Giusti, Enrico Maria Rigoni, Rudi Sergo & Daniele Fausti

  3. Department of Physics, University of Erlangen-Nürnberg, Erlangen, Germany

    Angela Montanaro, Francesca Fassioli & Daniele Fausti

  4. International School for Advanced Studies (SISSA), Trieste, Italy

    Francesca Fassioli

  5. Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany

    Stephan Winnerl

  6. CNR-IOM, TASC Laboratory, Trieste, Italy

    Simone Dal Zilio

  7. Jožef Stefan Institute, Ljubljana, Slovenia

    Dragan Mihailovic & Peter PrelovÅ¡ek

  8. Institute of Theoretical Physics, University of Hamburg, Hamburg, Germany

    Martin Eckstein

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Contributions

G.J., S.Y.M. and A.M. performed the experiments with support from F.G. and E.M.R. G.J. analysed the data with support from S.Y.M. M.E., D.F. and F.F. conceived and developed the theoretical models with support of D.M. and P.P. G.J. performed the finite-element simulations of incoherent thermal heating. R.S. developed the micrometric thermocouple junction for the temperature measurements within the cavity. S.D.Z. fabricated the silicon nitride membranes and the semi-reflecting cavity mirrors. D.M. provided the 1T-TaS2 samples. S.W. provided the THz emitters and guided the THz set-up. G.J., D.F., A.M., M.E. and F.F. wrote the paper with contributions from all the other authors. D.F. conceived and managed the project.

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Correspondence to Daniele Fausti.

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Extended data figures and tables

Extended Data Fig. 1 Experimental set-up.

a. Sketch of the THz time domain spectrometer. In the inset, the photograph of the tunable cryogenic cavity composed of two cryo-cooled moving mirrors within which the sample is embedded. b. Free-space nearly single-cycle THz field employed in the experiments detected trough Electro-Optical Sampling (EOS) in a 0.5 mm ZnTe crystal. c. Fourier transform of the nearly single-cycle THz field in free space. In the inset, the Fourier spectrum is plotted in logarithmic scale to highlight the spectral content of the THz field up to ∼ 6 THz. The black dashed line in the logarithmic plot indicates the noise level.

Extended Data Fig. 2 THz characterization of the empty cavity.

a. Time domain THz fields measured at the output of the empty cavity for three representative cavity frequencies \({\omega }_{c}\) indicated in legend. b. Cavity transmission spectra calculated from the fields shown in a. proving the tunability of the cavity fundamental mode.

Extended Data Fig. 3 Dependence of the observed metal-to-insulator phase transition on the waiting time.

The temperature evolution of the low frequency transmission (0.2 THz < ω < 1.5 THz) is plotted for different waiting times before starting the THz acquisition.

Extended Data Fig. 4 Determination procedure of the effective critical temperature of the metal-to-insulator transition.

a. In the top panel the temperature evolution of the integrated low frequency transmission (0.2 THz < ω < 1.5 THz integration range) upon heating and cooling (circled markers). The solid line is the result of an interpolation. In the lower panel the derivative of the interpolated curve whose maximum sets the effective critical temperature of the phase transition. b. In the top panel the temperature evolution of the integrated 1.58 THz phonon transmission (1.53 THz < ω < 1.62 THz integration range) and its interpolation. In the lower panel the derivative of the interpolated phonon response across the phase transition.

Extended Data Fig. 5 Cavity-induced renormalization of the free energy of the metallic phase.

a. Free energy model setting. Upper panels: coplanar cavity with a thin slab of matter (thickness d) inside a cavity of length \(L\). Lower panels: Sketch of the cavity modes dispersion and of the absorption solid band (green shaded region centered at \({\omega }_{{diss}}\)). As \(L\) is increased, modes are pulled inside and below the absorption band of the solid. The cavity fundamental mode is indicated with \({\omega }_{c}(L).\) b. Dielectric loss spectrum \(\alpha {\prime\prime} (\omega \)) (\(\Omega \) = 15 GHz, \(\gamma \) = 20 GHz) employed for the calculations. The spectrum has been normalized by the static contribution to the polarizability \(\alpha (0)\). c. Renormalization of the metallic free energy \(\varDelta {F}_{m}\) as a function of the cavity frequency for different temperatures. The cavity frequencies \({\omega }_{c}\) are normalized by \(\Omega \) = 15 GHz. d. Renormalization of the metallic free energy \(\varDelta {F}_{m}\) as a function of the temperature for different cavity frequencies above and below resonance \({\omega }_{c}=\Omega \).

Extended Data Fig. 6 Cavity control of sample dissipations.

a. Schematic representation of the thermal loads on the sample determined by its coupling with the cold finger through the cavity-independent factor \({K}_{\mathrm{ext}-\mathrm{int}}\) and with the photon thermal bath through the cavity-dependent factor \({K}_{\mathrm{ph}-\mathrm{int}}({\omega }_{c},Q)\). b. Density of states of the solid (peaked at the mode frequency \(\Omega \)) and of the cavity (peaked at multiples of the fundamental mode \({\omega }_{c}\)). The cavity density of states is multiplied by the Boltzmann distribution at the temperature of the photon bath \({{\rm{T}}}_{{\rm{ph}}}\) = 300 K. c. Dependence of the temperature ratio \({{T}_{\mathrm{int}}\left({\omega }_{c},Q\right)/T}_{\mathrm{ext}}\) as a function of the cavity frequency for different temperatures of the cold finger \({{\rm{T}}}_{{\rm{ext}}}\). The absolute temperature renormalization scales with \({K}_{\mathrm{ph}-\mathrm{int}}({\omega }_{c},Q)\). d. Evolution of the temperature ratio \({{T}_{\mathrm{int}}\left({\omega }_{c},Q\right)/T}_{\mathrm{ext}}\) upon tuning the cavity frequency for different values of the cavity-independent coupling constant \({K}_{\mathrm{ext}-\mathrm{int}}\) at a fixed cold finger temperature \({{\rm{T}}}_{{\rm{ext}}}\) = 80 K. The values of the cavity-independent constant \({K}_{\mathrm{ext}-\mathrm{int}}\) indicated in the legend have been normalized by \({K}_{\mathrm{ph}-\mathrm{int}}({\omega }_{c},Q)\) evaluated at \({\omega }_{c}=\Omega \).

Extended Data Fig. 7 Temperature measurements set-up.

Photograph of the micrometric Cr-Al junction sealed within the membranes and in thermal contact with the sample.

Extended Data Fig. 8 Finite elements simulation of the membrane’s thermal dissipations in free space.

a. Simulated 2D temperature profile of the membrane in free space. b. Radial dependence of the membrane’s temperature held in free space. The cold finger temperature has been set at \({{\rm{T}}}_{{\rm{ext}}}\) = 180 K.

Extended Data Fig. 9 Finite elements simulation of membrane’s temperature as a function of the mirror mounts position.

a. 3D thermal profile of the membrane for two representative distances between the mirror mounts (13 mm and 1.0 mm). b. Cut of membrane’s thermal profile along the radial direction for the two mounts distances presented in a. The cold finger temperature has been set at \({{\rm{T}}}_{{\rm{ext}}}\) = 180 K, as well as the mounts temperature.

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Jarc, G., Mathengattil, S.Y., Montanaro, A. et al. Cavity-mediated thermal control of metal-to-insulator transition in 1T-TaS2. Nature 622, 487–492 (2023). https://doi.org/10.1038/s41586-023-06596-2

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