Ultrafast melting and recovery of collective order in the excitonic insulator Ta2NiSe5

The layered chalcogenide Ta2NiSe5 has been proposed to host an excitonic condensate in its ground state, a phase that could offer a unique platform to study and manipulate many-body states at room temperature. However, identifying the dominant microscopic contribution to the observed spontaneous symmetry breaking remains challenging, perpetuating the debate over the ground state properties. Here, using broadband ultrafast spectroscopy we investigate the out-of-equilibrium dynamics of Ta2NiSe5 and demonstrate that the transient reflectivity in the near-infrared range is connected to the system’s low-energy physics. We track the status of the ordered phase using this optical signature, establishing that high-fluence photoexcitations can suppress this order. From the sub-50 fs quenching timescale and the behaviour of the photoinduced coherent phonon modes, we conclude that electronic correlations provide a decisive contribution to the excitonic order formation. Our results pave the way towards the ultrafast control of an exciton condensate at room temperature.

In these supplementary notes, we report additional details of the experimental methods and data analysis introduced in the main text.
In Note 1, we present the effect of the probe polarisation on the ΔR/R signal. Additionally, we show the temperature dependent data collected using probe pulses polarised orthogonal to the Ta and Ni atomic chains (along the c axis, see Fig.1b in the main text).
In Note 2, we discuss the model used to fit the kinetics of the signal in the NIR wavelength range.
In Note 3, we report the temperature dependence of the signal amplitude at wavelengths different from that used in the main text.
In Note 4, we describe how time zero is determined in our measurements and show the details of the ΔR/R signal around this time delay.
In Note 5, we present the calculation of the out-of-equilibrium optical conductivity of the material to analyse the change in spectral weight at 1200 nm in the presence of strong photoexcitation or high temperatures.
In Note 6, we investigate the effect of temperature on the threshold fluence required to melt the excitonic order.
In Note 7, we discuss in more detail the behaviour of the Δ(ΔR/R) signal amplitude as a function of ΦP1.
In Note 8, we present the temperature and fluence dependence of the 1 THz phonon mode deduced from two-pulse measurements.

Note 1 -Effect of probe polarisation
The transient reflectivity signal of Ta2NiSe5 in the visible and near infra-red (NIR) region strongly depends on the orientation of the probe polarisation, as it is expected from equilibrium optical measurements 1,2 . Supplementary Fig. 1a shows the ΔR/R spectra (averaged between 0.5 and 1 ps) collected for probe polarisations along the a and c axis at room temperature and using a pump fluence Φpump = 45 µJ/cm 2 . We attribute this drastic difference to the strong 1D nature of Ta2NiSe5, which implies that different probe polarisation are sensitive to different electronic transitions.
In Supplementary Fig. 1b we present the evolution of the transient reflectivity spectra as a function of temperature for a probe polarisation along the c axis. The signal in the NIR shows a strong temperature dependence but, contrary to the behaviour presented in Fig. 1b of the main text, it does not appear to saturate as the temperature rises above Tc. Remarkably, the signal in the visible range shows no dependence on the temperature. Further studies are required to determine the nature of the electronic transitions involved in the material's optical response and their relationship to its electronic properties.

Note 2 -Fitting model
The fit of the electronic (incoherent) component of the signal for all temperatures and fluences is hindered by the drastic change in the kinetics as a function of these physical quantities. For this reason we are not able to provide a complete quantitative analysis of all fitting parameters. We focus instead only on the value of the signal amplitude, whose behaviour is not influenced by the specifics of the fitting function used. In addition, we employ this fitting procedure to isolate the coherent component of the signal associated to the phonon oscillations.
We consider a functional form commonly used to describe the transient optical response in condensed matter systems 3,4 : The terms in curly brackets are associated to the rise and decay of the signal at early times (< 2 ps) and to the slow signal growth at long times (> 2 ps) respectively. In particular, 1 and 2 are the amplitudes of these two components, the error functions describe the rise of the signal with characteristic time ,1 and ,2 , and the exponential term captures the signal decay with characteristic time .
In Supplementary

Note 3 -Wavelength dependence of temperature behaviour
In Supplementary Fig. 3 we show the dependence of 1 as a function of temperature (in analogy with the plot in Fig. 1d of the main text) for the 800 nm component of the probe pulse. The behaviour is the same previously observed in other works 4,5 and is different from that observed in the NIR region. This underscores the uniqueness of the wavelength region investigated in our work, which allows us to easily follow the evolution of the excitonic order.
In Supplementary Fig. 4 we present the dependence of 1 as a function of temperature for two additional wavelengths in the NIR. As mentioned in the main text, the precise temperature at which the signal switches sign shifts slightly as a function of the probe wavelength, but the overall behaviour is consistent across the NIR range detected in our measurements. We note that the dashed line is obtained with the same equation used in the main text, in particular using the same value for Tc = 328 K. Supplementary Fig. 3. Amplitude of the ΔR/R signal as a function of temperature for a 800 nm probe wavelength. The observed behaviour is analogous to that reported in Fig. 3a

Note 4 -Time zero, coherent artefact and free-induction decay
In our broadband measurements the probe pulse reflected by the sample is collected and dispersed onto a CCD camera to achieve spectral resolution. As the pulse is naturally chirped each spectral component arrives at the detector at slightly different times. In particular, in our measurements, the longest wavelengths are at the front of the probe pulse while the shorter ones trail.
For what concerns the pump-probe measurements, we define time zero as the probe delay for which the transient reflectivity signal (after the coherent artefact, see below) becomes visible at the shorter wavelengths, that is when the pump pulse "catches up" with the tail of the probe pulse. The signal is then chirp-corrected in the data analysis stage to report all the wavelength components with their correct time zero, as it is commonly done in broadband pump-probe spectroscopy 7 . In the three-pulse experiments we find time zero by performing the same procedure on P1 and P2 separately.
We note that the transient reflectivity is not identically zero before a time zero determined as described above. As shown in Supplementary Fig. 5, the signal instead shows oscillations that are particularly visible at the higher excitation fluences. The largest feature right before time zero is the so-called coherent artefact occurring when pump and probe pulses overlap in space and time in the material 8 . The smaller oscillations are also a well-known effect, arising particularly in experiments that use ultra-short excitation pulses. It is typically referred to as perturbed free-induction decay and does not carry any obvious information on the material 9 . When we focus on the analysis of the ΔR/R signal at early times we cut out this "signal" before time zero to simplify the understanding of our discussion. Supplementary Fig. 5. Signal rise as a function of fluence. Normalised Δ(ΔR/R) signal (analogous to that reported in Fig. 2b) at short probe delays and before time zero.

Note 5 -Time-resolved evolution of the optical conductivity
In the main text, we explain that the peculiarity of the spectral region around 1200 nm (1.03 eV) might be associated to a shift in the spectral weight of the system's electronic as the excitonic condensate is melted. This interpretation is substantiated by previously published work on the temperature dependence of the real part of the optical conductivity ( 1 ) of Ta2NiSe5 10 . In the equilibrium data reported there, a clear feature centred around 1.05 eV (that we refer to as F1eV in the following) is observed below Tc, while it is completely suppressed at high temperatures. The spectral weight associate to this feature could then be connected to electronic states only available when the excitonic gap is open (and therefore spectral weight is shifted up from the low energy scale).
To shed more light on this physical process and to support our conclusions, we used the equilibrium data (that the group of Professor A.V. Boris at the Max Planck Institute for Solid State Research kindly shared with us) together with our pump-probe signal to reconstruct the time evolution of 1 . In particular, we compare how this quantity evolves after the material is perturbed at room temperature in the presence of a weak and strong pump pulse, and at a temperature above Tc.
As mentioned above, we begin with the equilibrium 1 at the temperature of interest as measured in [10]. Using a Kramers-Kronig constrained variational analysis 11 , we can then extract the equilibrium reflectivity ( 0 ( )) of the sample. Turning now to our pump-probe measurements, the signal that we collect is ∆ ( , ) 0 ( ) ⁄ = ( , ) 0 ( ) − 1 ⁄ . Using the calculated 0 ( ), we can therefore obtain the reflectivity of the material ( , ) for every value of the pump-probe delay. Finally, using a differential Kramers-Kronig constrained variational analysis step 12 , we can calculate the time dependent optical conductivity 1 ( , ).
In Supplementary Fig. 6, we report the result of this analysis applied to the room temperature pump-probe data with Φpump = 26 µJ/cm 2 . In Supplementary Fig. 6(a), we plot 1 over the energy range between 0.9 eV and 1.7 eV. Here, we see that the region around F1eV shows the largest time dependent change in these conditions. In Supplementary Fig. 6(b) we focus on this region to inspect the effect of the pump perturbation more closely. At this low fluence, F1eV clearly exists at all times in the optical conductivity. The feature is marginally suppressed immediately after photoexcitation and returns to the equilibrium condition at long delays. This is the behaviour that one would expect in the presence of a perturbation process that partially suppresses the excitonic order.
In Supplementary Fig. 7(a,b) we show the result of the same calculation for the case of T = 343 K (the highest temperature for which the equilibrium data is available) and Φpump = 176 µJ/cm 2 . We choose to focus on a higher fluence than in the room temperature case because the ΔR/R signal is much smaller above Tc. Here, we see a very different behaviour for 1 . As we mentioned, the equilibrium optical conductivity does not include F1eV at this temperature. The time dependent 1 increases after photoexcitation uniformly across the whole energy range, a behaviour compatible with the temporary enhancement of a Drude component to 1 induced by the excitation of quasi-particles across the energy gap. This appears to be the strongest contribution above Tc.
We now have all the necessary elements to analyse the material's response at room temperature and in the presence of a high excitation fluence (see Supplementary Fig. 7(c,d) for the case of Φpump = 705 J/cm 2 ). In this case we see that 1 very rapidly evolves to resemble the high temperature response. In particular, F1eV is completely suppressed within ~ 125 fs and the response is dominated by a Drude-like increasing 1 at pump-probe delays up to ~ 1.5 ps. At even longer delays we witness a recovery of F1eV and 1 progressively approaches the equilibrium curve, with a slightly more pronounced tail at higher energies that could be associated to the onset of a bolometric effect.
The results presented here support our conclusion that the optical response of Ta2NiSe5 at 1200 nm mirrors the low-energy physics of this system. In particular, we demonstrate that, in the presence of a strong photoexcitation, the transient optical conductivity becomes analogous to the equilibrium one at temperatures above Tc. We can therefore use the ΔR/R signal to track the status of the excitonic condensate as explained in the main text. We stress that this is not