To map out the temporal phase diagram we link STM images of different phases with the femtosecond optical spectroscopy results. First, we identify which long-lived nonequilibrium phases we can reach with different photoexcitation densities. To this end, we conduct STM experiments at low temperatures (4 K), where all of the previously known photoinduced phases can be considered stable, and we can distinguish them by their distinct spatial electronic ordering. Next, we link the latter to specific coherent phonon spectral features measured with the low-fluence two-pulse transient reflectivity spectroscopy. With the phonon fingerprints of the various states ascertained, we present three pulse technique measurements designed to track the non-equilibrium phonon evolution on short timescales.
STM experiments. We use an ultrahigh vacuum (UHV) low temperature STM (LT Nanoprobe, ScientaOmicron) with optical access (Figure 1a). The 1T-TaS2 samples are excited with an external laser. Since the STM scans cover a very small ( nm2) area of the elliptical Gaussian laser spot ( μm2 at FWHM) we can investigate the effect of different laser fluences simply by choosing an appropriate area of the STM scan with respect to the center of the Gaussian beam. The excitation is done with a laser pulse with the peak fluence of 12 mJ/cm2, which gives us a possibility to perform STM measurements over a wide range of fluences = 0~12 mJ/cm2 (Figure 1a). Typical experiments are done with a single laser pulse photoexcitation, but multiple pulse excitations were also performed to understand the effects of heating the sample. The outcome of different 1 and 106 shot experiments are shown in Figures 1c and 1d, where the colors of triangles represent the different observed states (Figures 1e-j). In both cases, the system returns to the original (C) state after photoexcitation (Figure 1e, blue in 1c and 1d) in the region where the fluence 1.5 mJ/cm2. Above mJ/cm2 the characteristic H state domain mosaics19 consistently appear (Figure 1f, yellow in 1c and 1d), independent on the number of the excitation pulses. Increasing the fluence beyond mJ/cm2 patches of the amorphous A state with a characteristic hyperuniform electronic structure18 start to appear within the H-state areas (Figure 1g, pink in 1c and 1d). These appear very inconsistently, and independent of the number of excitation pulses. At even higher fluences, we observe irreversible structural changes (ISC) that cannot be annealed by heating the sample (black). These include single layer polytype transformations from 1T to 1H (Figure 1h), which appear as triangular patches of various sizes without charge ordering above 70 K17. Another form of ISC is the layer peel-off and the creation of 1D nanotube-like objects (Figure 1i). Eventually melting/ablation of the material is observed and an uneven surface is created with nano-scale modulations (Figure 1j) or craters a few microns in diameter (Figure 1b). Large regions of ISC sometimes appear in single pulse experiments, but are more common with pulse-train excitation (Figure 1d) (Figure 1c shows an example of a single pulse excitation, where ISC did not appear, however this is not always the case), implying that the accumulated heating of multiple pulses enhances the formation of ISC. The ISC areas are surrounded and sometimes intermixed either by H or A state on micrometer scale regions. We further note that for high fluences > 3 mJ/cm2 the transition outcome is not perfectly reproducible on different areas of the sample. We attribute this to uneven thermal coupling between the sample and the substrate, possible imperfections of the layer stacking, or strains caused during cleaving.
Femtosecond laser spectroscopy. Having established the boundaries of the phase diagram on the STM timescale of ~103 s, we use femtosecond spectroscopy with three different pulse sequences (Figure 2a) to investigate the trajectory of the system on the timescale down to 10-13 s via coherent phonons: (i) A single “Driving” (D) pulse causes the change of state, followed by a standard stroboscopic two-pulse Pump (P) - probe (p) experiment, in which the timescale is defined by the total time of the measurement (~10 minutes). The weakly-perturbative P-p protocol allows us to extract the near-equilibrium phonon fingerprints of the metastable phases on the same timescales and temperatures as in the STM experiments, thus matching the signatures obtained by the two techniques. (ii) A repetitive three-pulse D-P-p sequence gives access to the picosecond timescale. Here, each scan of the P-p experiment is taken with a small (ps) fixed delay between the D and P pulses. This is applicable for mapping the H state at temperatures where its lifetime is shorter than the repetition time (1 ms using a 1 kHz laser system) and thus the sample fully relaxes before the next D-P-p sequence arrives. (iii) The D-P-p technique, with the changed order of the pulses. Here the P-p pulses come a few tens of ps before the D pulse, which effectively produces ~ 1ms D-P delay (defined by the repetition rate). This way, we are able to establish whether the sample has relaxed between the pulses or in the case that it has not relaxed, we are able to see which state was present after 1 ms. To ascertain that no permanent change has occurred in the sample in the case when it does not completely relax in 1 ms, we turn off the D pulse and re-measure the reflectivity transient using only the weakly perturbative P-p sequence.
The C and H states can be distinguished by the frequency of the collective amplitude mode (AM)13. While the AM frequencies in both states are temperature dependent, the AM frequency of the H state is about 0.1 THz lower than the AM frequency of the C state at any given temperature27, thus making the two states easy to distinguish. The T and NC states show a characteristic double peak in the phonon spectrum with lower amplitude and about 0.1 THz lower frequency than the H state at any temperature and can thus also be clearly differentiated27. In Figure 2a and b we show the transient reflectivity oscillations and the respective Fourier spectra for C, H and T states. A detailed analysis of the C, H, NC and T state AM peak frequencies and line shapes with multi phonon fits and their temperature dependences are given in Reference 27.
The data for different D pulse fluences mJ/cm2 were taken at 80, 100, 140, 160 and 200 K. In Figure 2c and d we show the transient reflectivity oscillations and the respective Fourier spectrum at 160 K at different D fluences after 30 picoseconds and after a millisecond after switching to the metastable state.
Following the difference between the AM peaks in the C and H state, the C/H boundary on the low-fluence side can be defined with a high degree of certainty. The photoinduced H state at fluences slightly above 1 mJ/cm2 forms already on the picosecond timescale and relaxes at this temperature within the ~1 ms time between the pulses. The same was observed at 100 K and 140 K. At 80 K, the H state does not completely relax between the succesive pulses, which is in agreement with the STM data at 77 K.
On the high-fluence side, the boundary of the H state cannot be as clearly ascertained. With increasing fluence, we see lowering of the AM peak intensity, broadening of the peak and a further shift to lower frequencies. In this regime, we cannot easily recognize a unique fingerprint of any of the known states. To ascertain the presence of the A state, we compare the spectra of pristine and exposed samples 1 ms after photoexcitation at high temperatures, where the contribution of H phase is absent due to its short lifetime. We see that for fluences above mJ/cm2 the sample does not relax completely to the C state in 1 ms, which is expected for the A state, but may also appear when other unidentified long-lived disordered phases or phase separation are present. As observed by STM for mJ/cm2, such transient states with no characteristic oscillation fingerprint eventually evolve into either the H or the A state. Since (i) multiple pulse experiments in STM show little or no difference from single pulse experiments (with fluences below the damage threshold) and (ii) repetitive single-shot measurements in the same spot in STM show different electronic ordering pattern of the H and A states after each pulse, we conclude that the final photoinduced states are ‘reconfigured’ by each pulse and independent of the initial electronic order.
For mJ/cm2, the AM peak intensity decreases even further, indicating the appearance of ISC. The irreversibility of the excitation process was tested by turning off the D pulse and measuring a control P-p transient from the same spot. At fluences up to 7 mJ/cm2, the signal mostly recovers. With increasing the fluence beyond 7 mJ/cm2, the signal recovers only partially, while finally, at fluences above 10 mJ/cm2, the sample suffers enough damage to completely suppress the signal, which is consistent with the STM scans.
The time-domain phase diagram with a compilation of the transition outcomes for different F and T is shown in Figure 3, combining STM (triangles) and transient reflectivity data (squares). The time-axis signifies the time after the photoexcitation pulse (Figure 3a) grouping the data into three timescales: ultrashort ( s), intermediate ( s) and long ( s). The F axis is converted into the photon density taking a penetration depth of 30 nm at 800 nm (Figure 3b). The color shade (blue, yellow, pink, black) represent different states as shown in Figure 1e) – j). White represents unidentified transient states, or an inhomogeneous mixture of states, which cannot be separated spectroscopically.
We see that the H state has a nearly temperature-independent threshold fluence and is stable at low temperature in agreement with Ref. 3. When the measurement timescale is longer than the relaxation time, the H state disappears, thus the C/H boundary moves to lower temperature with time. The phase boundary of the C state observed by TRED32 agrees remarkably well with the present measurements on short timescale. Also, the suppression of the CDW diffraction peaks is in agreement with the decrease of the AM peak intensity in the transient optical spectroscopy data reported here27,32. Finally, we note that the H state boundaries on long timescales are also consistent with the recent XRD measurements37. Comparing the appearance of the H state on short and long timescales we see that the H state immediately appears at low fluences, but it takes much longer to stabilize at higher fluences. On the other hand, on the long timescale at 77 K the H state is only visible at fluences above ~5 mJ/cm2, but is absent at lower fluences, even though it was observed there on a short timescale. This implies that the relaxation first happens on the outskirts of the beam, where the excitation fluence is lower.
To obtain insight into the origin of different phases we compare the observed experimental phases on the STM timescale with the equilibrium configurational states obtained from theoretical treatment. The model considers the ordering of electrons subject to screened Coulomb interaction on a triangular atomic lattice, and was previously successfully applied to describe both irregular domain patterns24,25 and hyperuniform polaron orders18,24 in the H and A states, respectively. It’s predictions can be compared with the experiment by assuming a correspondence between the photoexcited carrier density (which is proportional to incident photon density) and electron filling. The model defines the filling of the system as the number of electrons at the Fermi level divided by the number of atoms24. In 1T-TaS2 with one electron per Ta atom, a reconstruction of the CCDW state gaps 12 out of 13 electrons, resulting in 1/13 filling by the remaining electron38,39. Doping is defined as a change of the filling with respect to 1/13. Experimentally, the filling is obtained by counting the number of polarons per unit area in an STM image (1 polaron equals 1 electron) 18,24.
Monte-Carlo simulations using this model give a theoretical phase diagram (Figure 3c) that is consistent with the experimentally observed C (1/13 filling) and H states at ~ 4 % nominal doping 24,25, observed at the experimental photodoping of 0.09 photons/unit cell. Remarkably, they also predict the A state towards 1/11 filling (at nominal doping, observed at a threshold of ~0.3 photons/unit cell) 18,24. Simulations also predict the existence of a uniform ordered state with 1/12 filling and close to 1/12 domain states around it, but these states are not observed experimentally. Possibly, the 1/12 superlattice is less stable and may only exist as a transient phase, but so far it has not been observed. In spite of the crudeness of the simple model, which correctly predicts the observed metastable charge configurations, we cannot expect it to predict their stability, for which one needs to consider additional effects, such as long-range order and topological defects created in the transition19. Larger density of such defects created by higher fluences may be the cause of the higher long-term stability of the metastable H phase at higher fluences, which was observed at 77 K. The amorphous state on the other hand is stabilized by the constraints imposed by jamming, which is an entirely different stabilization mechanism18.
We conclude that by a carefully chosen combination of techniques, phase-diagram ‘snapshots’ can be obtained during the relaxation trajectory of a non-equilibrium system. Comparison of the experimental phase diagram with the theory under the assumption that photoexcitation is equivalent to doping confirms that three out of four phases can be reached with photoexcitation fluence as the only control parameter. While the transition outcome reproducibility is excellent on the low-fluence side (up to ~3 mJ/cm2), various factors that are not under direct control contribute to variable transition outcomes on the high fluence side. This has important implications for the stability and potential device reliability. The understanding of the time-evolution of different nonequilibrium states revealed by temporal phase diagrams opens the way to the development of new functionalities in metastable quantum materials based on configurational electron ordering.