Overcoming the thermal regime for the electric-field driven Mott transition in vanadium sesquioxide

The complex interplay among electronic, magnetic and lattice degrees of freedom in Mott-Hubbard materials leads to different types of insulator-to-metal transitions (IMT) which can be triggered by temperature, pressure, light irradiation and electric field. However, several questions remain open concerning the quantum or thermal nature of electric field-driven transition process. Here, using intense terahertz pulses, we reveal the emergence of an instantaneous purely-electronic IMT in the Mott-Hubbard vanadium sequioxide (V2O3) prototype material. While fast electronics allow thermal-driven transition involving Joule heating, which takes place after tens of picoseconds, terahertz electric field is able to induce a sub-picosecond electronic switching. We provide a comprehensive study of the THz induced Mott transition, showing a crossover from a fast quantum dynamics to a slower thermal dissipative evolution for increasing temperature. Strong-field terahertz-driven electronic transition paves the way to ultrafast electronic switches and high-harmonic generation in correlated systems.


Supplementary Methods. THz pump-SWIR probe setup
We use the output of a 100 Hz, 20 mJ, 45 fs Ti:Sapphire laser to drive an optical parametric amplifier (OPA) which provides both signal and idler beams. The signal spectrum is centered at 1.5 μm while the idler at 1.8 μm. The idler was splitted in two beams before the sample; the first beam was used to probe the transmission of the sample (SWIR probe) while the second one was measured by a reference detector to implement the differential detection scheme (see Supplementary Fig. 1a). The spot size of the probe beam on the sample is 68 μm (1/e 2 width).
Single-cycle THz pump pulses were generated from the OPA signal beam by optical rectification in DAST crystal 1 . Metal mesh low-pass filter, inserted into the optical path of the THz, was used to cutoff frequencies higher than 6 THz. The maximum THz energy for the experiment was =9.6 μJ.
THz beam was focused on the sample inside a cryostat (Montana Cryostation) by a parabolic mirror with a focal length of 3 inch. The beam focus measured by a THz camera (NEC Terahertz Imager) is shown in Supplementary Fig. 1b (blue curve). The spot size is 276 μm (1/e 2 width), which corresponds to a fluence onto the sample of 16 mJcm -2 . The THz pulse temporal profile measurement at the sample position was performed by electro-optic sampling (EOS) using a (110) GaP crystal with a thickness of 50 μm. The measured full-width half maximum THz pulse duration is =0.166 ps. The electric field strength = √ 0 =8.0 MVcm -1 has been calculated from peak THz intensity 2 : where is the beam waist.
At this electric field strength (F=16 mJcm -2 ), no damage has been observed on the V2O3 film for both insulating and metallic phase. High intensity THz measurements were carried out focusing the THz beam by means of a parabolic mirror with 2 inch focal length. The beam profile on the focus is shown in Supplementary Fig. 1b (1/e 2 width 180 μm), red curve, which corresponds to a fluence of 37 mJ/cm 2 and to a THz electric field strength of 12.7 MVcm -1 . At this electric field, in the metallic phase we observed micro-cracking damage due to THz driven electrostriction as discussed in the main manuscript. Additional SEM images of the micro-crack details in V2O3 thin film are reported in Supplementary Fig. 2.
(1) Supplementary Fig. 2: Critical strain and damage induced by THz pulse on metallic V2O3. SEM images of the micro-crack details in V2O3 thin film. The high current density driven by an intense THz pulse induces stress waves on the film surface propagating along the electric field direction (red arrows). For an electric field of 12.7 MV/cm, the critical shear stress results in a group of micro-cracks which follow the equipotential lines of the THz field. An accumulation of material is also observed at the edges of the cracks due to the strong mechanical stress. (Number of shots, N=10000).

Supplementary Note 1. Optical conductivity of V 2 O 3 thin film in steady state regime
The temperature evolution of the electrodynamics properties in the mid-infrared to optical region across the insulator-to-metal transition of the V2O3 film was characterized by measuring the optical transmittance using Fourier transform infrared (FTIR) spectroscopy. The real part of the optical conductivity 1 vs frequency, depicted in Supplementary Fig. 3a, is calculated by the Tinkham formula 3,4 = 1 (1 + 0̃/ ( + 1)) 2 ⁄ , where 0 = 377 Ω is the vacuum impedance, is the thickness of the V2O3 film, is the refractive index of the substrate and ̃ the complex optical conductivity of the V2O3. For the V2O3, in our spectral range the contribution of the imaginary part of ̃ to the transmittance is negligible, therefore is reasonably to assume = 1 (1 + 0 1 /( + 1)) 2 ⁄ . The insulating monoclinic phase (Θ < Θ = 150 ) shows an energy gap > 0.6 eV 5 approximately related to the transition between and 1 bands. When the IMT is concluded, the metallic phase is characterized by a Drude-like lineshape in agreement with previous measurements 5 . The Tinkham formula is applicable if / < 1 (with frequency of light; speed of light; sample thickness; refractive index of V2O3). In both metallic and insulating phase, this condition is always satisfied at the probe wavelength 6 . In Supplementary  Fig.43 we compare the optical conductivity by Tinkham formula (panel a) with the one computed by the Kramers-Kronig (KK) constrained analysis (panel b) which provides the exact solution 7 . The good agreement of these two results further confirms the applicability of the Tinkham formula. Supplementary Fig. 3: Temperature dependence of the real part of the optical conductivity calculated using the Tinkham formula (a) and Kramers-Kronig (KK) constrained analysis (b) from the transmittance measured by FTIR. Dashed line indicates the probe frequency. Inset: Comparison of the two methods at the probe wavelength. The small peak between 3200 cm -1 and 3700 cm -1 is from the not perfect compensation of the transmission measurements. It is related to the O-H stretching mode of the water because the FTIR measured were carried out with the cryostat at normal air conditions. Supplementary Fig. 4 IMT dynamics vs. the pump spectrum. a, Electric field profile of the THz pump pulses: pump pulse with the full-band spectrum used in the main manuscript (blue curve) and spectrally limited to 3.7 THz. Inset: relative spectra which are far below the phonon band of V2O3 (green curve). The optical conductivity is related to bulk single crystal of V2O3 11 . b, Temporal evolution of transmission modulation at = 4 driven by a THz pump with spectrum used in the main experiment (blue curve) and driven by a THz pump with a spectral cut-off at 3.7 THz (red curve). The THz electric field strength is ~4 MVcm -1 . .

Supplementary Note 2. Ultrafast IMT by THz non-resonant pumping
As discussed in the main text, the terahertz field acts as off-resonant excitation with photon energy below the lattice phonons and the interband transitions. In order to exclude any possible resonant excitation with the lattice as mechanism to drive the transition, the transmission modulation of the SWIR probe was measured reducing the pump spectrum to 3.7 THz by means of a THz low-pass filter (see Supplementary Fig. 4a). In Supplementary Fig. 4b, the temporal traces of -ΔT/T are reported for the two different THz pumps. As one can clearly observe, the pump-probe dynamics is comparable for the two THz pumps and it is appreciably independent of the spectral content of the pump (which are both below the phonon band). Thus we can conclude that the IMT is driven by a non-resonant THz excitation.
Finally, we can exclude a multi-photon process involving optical phonons in driving the IMT. As the latent heat of the V2O3 associated to the first order structural transition is 70 mJcm -3 (see Ref. 8), for the illuminated sample volume in our experiment (thickness 82 nm, diameter 276 μm), we can estimate that an energy of 0.024 uJ is required to carry out the transition involving optical phonons. The THz pump energy in our experiment is 9.6 μJ. We can roughly estimate that the efficiency of the multi-photon excitation must be 10 -3 to achieve the IMT. In our knowledge, no multiphoton process of up-conversion (especially at THz frequency) has such conversion efficiency. This suggests that the increase of phonon population by multi-phonon processes does not play a role in the ultrafast IMT.

Supplementary Note 3. THz-induced nucleation dynamics
Close to the IMT temperature (at Θ = 115 ), the optical conductivity increases and the current generated by the THz pump prevents the tunnel mechanism. Due to the Joule heating, as discussed in the main text, the sub-ps insulator to metal switching is replaced by a slow thermal dynamics. The temporal evolution of -ΔT/T, associated to the nucleation and growth of the metallic domains, shows an exponential evolution with a rise-time of ~28 ps as shown in Supplementary Fig. 5.

Supplementary Note 4. Nonlinear THz transmission of the V 2 O 3 thin film at 4 K in the high field regime
Even at the minimum temperature (4 K), after a fast rise due to the tunneling processes the dynamics shows a slow increase related to the thermal nucleation of the metallic phase caused by THz induced electronic heating (see Fig. 2a-b in the main manuscript).
In order to estimate the dissipated THz energy we measure the THz transmission of the V2O3 film at 4 K as a function of the THz electric field strength (see setup in Supplementary Fig. 6). Nonlinear THz transmission modulation vs. THz electric field was measured tuning the amplitude of the THz electric field with a pair of wiregrid polarizers (WGP1 and WGP2 in Supplementary Fig. 6). The transmitted intensity of the sample and reference was detected by a Golay cell (THz detector in Supplementary Fig. 6). We observed an exponential decrease of the THz transmission (increase of -T/T) due to the THz driven metallization. At the maximum electric field, we observe a decrease of the transmittance of ~6%. By means of Reffit software 7 , we estimate an optical absorption of ~5% which corresponds to a deposition on order of ~0.5 μJ of THz energy. This dissipated THz energy is comparable with the latent heat (0.34 μJ) associated to the first-order structural transition 8 . Therefore, it is realistic that, after the tunneling dynamics, the THz heating causes the thermal nucleation and the slow growth of the metallic phase as observed in Fig. 2a.

Supplementary Note 5. Increase in electronic temperature in metallic V 2 O 3 by THz joule heating
In the metallic phase (Θ > 145 ), the THz pump pulse enhances the electron energy through Joule heating leading to an increase of the electronic temperature Te which results in an increase in optical transmission (-T/T<0), as discussed in the main manuscript. Indeed, as V2O3 is a strongly correlated metal, the electronic correlations greatly renormalize the coherence temperature Tch~ 400 K. The rise of the electronic temperature Te, to Tch, causes a strong reduction of the Drude spectral weight 9 . Here, we evaluate the increase of Te by the THz energy density deposited in the sample and we show that it is compatible with the measured transmittance increase. The parameters of our experiment are: THz pulse energy: 9.6 μJ; initial background temperature: 175 K; V2O3 transmittance in THz range ~ 10%; Spot size (diameter 1/e 2 ): 276 μm; Sample thickness: 82 nm; V2O3 electron heat capacity at C(Te): γ Te, with γ=80 mJK -2 mol -1 (Ref. 10); V2O3 density 4.87 gcm -3 . At 175 K, we estimated a fast increase of the electronic temperature by THz Joule heating in the metallic phase of ΔΘ~200 K. For this temperature enhancement, infrared measurements show a drop of the NIR optical conductivity of 100÷300 Ω -1 cm -1 (Ref. 11), which is consistent with a transmittance variation -T/T of 10%.

Supplementary Note 6. THz pump SWIR probe Vs THz probe
In the insulating phase of V2O3, the optical gap Δ~0.6 eV is defined through the minimum energy difference between the 1 and bands. However, the small joint density of states of the interband transitions at 0.67 eV (photon energy of the SWIR probe), results in a negligible contribution to the optical conductivity (see Supplementary Fig. 7a). Indeed, the maximum of the interband contribution to the optical conductivity is located at ~1.2 eV (effective optical gap), far above the probe photon energy 5,12 . In the metallic phase, the optical response at the probe photon energy of 0.67 eV is mainly dominated by intraband transitions, which are related to the metallic behaviors. This behavior is described in Supplementary Fig. 7b, where we analyze the electrodynamics of paramagnetic metallic phase of V2O3 through a Drude-Lorentz multicomponent fit (see Ref. 13 for details). The red curve represents the:Drude + MIR band (as discussed in Ref. 13) while the vertical dashed black line shows the probe frequency (5500 cm -1 ). As one can observe, at the probe frequency, which is far below the Drude plasma frequency (ωp~11000 cm -1 ), the intraband contribution (metallic behavior) is the main contribution to the optical conductivity.