A time-domain phase diagram of metastable states in a charge ordered quantum material

Metastable self-organized electronic states in quantum materials are of fundamental importance, displaying emergent dynamical properties that may be used in new generations of sensors and memory devices. Such states are typically formed through phase transitions under non-equilibrium conditions and the final state is reached through processes that span a large range of timescales. Conventionally, phase diagrams of materials are thought of as static, without temporal evolution. However, many functional properties of materials arise as a result of complex temporal changes in the material occurring on different timescales. Hitherto, such properties were not considered within the context of a temporally-evolving phase diagram, even though, under non-equilibrium conditions, different phases typically evolve on different timescales. Here, by using time-resolved optical techniques and femtosecond-pulse-excited scanning tunneling microscopy (STM), we track the evolution of the metastable states in a material that has been of wide recent interest, the quasi-two-dimensional dichalcogenide 1T-TaS2. We map out its temporal phase diagram using the photon density and temperature as control parameters on timescales ranging from 10−12 to 103 s. The introduction of a time-domain axis in the phase diagram enables us to follow the evolution of metastable emergent states created by different phase transition mechanisms on different timescales, thus enabling comparison with theoretical predictions of the phase diagram, and opening the way to understanding of the complex ordering processes in metastable materials.

H state where the fluence is larger than 5.7 mJ/cm 2 (the observed area of the H state on the sample is smaller for the same laser beam). This is due to the faster relaxation of the H state at higher temperatures, which happens on the outskirts of the beam and prevents us from observing the whole switched area of H state with the relatively slow STM device. The observation could as well imply a higher switching threshold at higher temperatures, but the transient reflectivity measurements do not support this claim. Another important observation is that the observed switching fluence stays independent from the number of the incident pulses, both at 77 K and at 4 K. A very slight decrease in the threshold fluence (increase of the switched area) at 4 K with increasing the number of pulses is most likely the consequence of the spatial drift of the beam during long exposures. We conclude that the laser induced accumulated heating and nonequilibrium photoexcitations are well-separated effects.
Amorphous state. The amorphous state does not appear consistently across all experiments.
In some cases, it is observed in patches within a larger area of the H state, while in other cases it is mixed with ISC areas. At 4 K the amorphous state was found both surrounded by H state and mixed with ISC, while when excited at 77 K it was only found mixed with ISC. On heating the A state from 4 K above 77 K, it was found surrounded by the C state when not mixed by ISC. In contrast with the electric switching 1 , we have not found a way to controllably use optics to reproducibly switch the sample to the A state. However, we have found the boundary conditions at which the A state is likely to appear in optical experiments.
Irreversible structural changes. We observe no correlation between the sample temperature and the area of the induced ISC at the sample temperatures of 4 and 77 K (Supplementary Figure 2). However, the area of ISC increases with the number of laser pulses, implying that at large fluences the accumulated heating plays a more critical role as opposed to low fluences. In most cases the threshold fluence to induce ISC is between 7 and 10 mJ/cm 2 . This is particularly important for the polytype transformations 2 , which were never observed in a single shot experiment, as they are a consequence of heating the sample, rather than an ultrafast electronic process. The same experimental conditions (power, exposure time and temperature) that lead to the polytype transformation in one case can create a large visible hole in the sample in another case. Single shot experiments can also have different ISC outcomes. When switching the sample with a single shot at two well-separated positions on the same crystal, we did not observe any ISC in one case, while in the other case we were able to see ISC in the form of melted sample in the middle. In both experiments the peak fluence exceeded 10 mJ/cm 2 and the sample was held at 4 K. This clearly suggests that the outcomes at high fluences are strongly dependent on local properties of the sample, which are responsible for uneven sample cooling. The heat transfer is determined by the quality of the thermal coupling between the top layer(s) and the bulk sample and/or the sample holder. This varies with the amount of glue, the thickness of the sample and the interlayer structure, which are not very well controlled experimental variables.

Supplementary note 2. Transient reflectivity measurements
Transient reflectivity at 100 and 160 K. The first set of D-P-p measurements was done at 100 K, with the D-P delays of 400 ps, 30 ps, -3 ps and -30 ps and with the fluences ranging from 0.4 mJ cm -2 to 10 mJ/cm 2 (Supplementary Figure 4). In case where the D pulse arrives before the P-p sequence, we performed two separate sets of measurements, for the D-P delay of 30 ps and 400 ps. This way make sure that the observed state is not changing on the timescale of the measured P-p trace (30 ps). Since the excited states at tD-P = 30 ps and tD-P = 400 ps show the same characteristics, we conclude that they are stable on the 10-100 ps timescale and further consider only the measurements at tD-P = 30 ps.
One can notice the generally decreasing amplitude of the oscillations when increasing the D pulse fluence. Comparing the measurements of the millisecond state to picosecond state, we can see that the oscillation amplitude is at all fluences at least partly restored, suggesting that some sort of relaxation takes place even at the highest fluences. At fluences higher than 10 mJ/cm 2 a visible damage (a hole) was created and we were unable to perform any further measurements on that part of the sample. From the measurements, where the D pulse hits the sample during the P-Pr sequence (tD-P = -3 ps) we see that above a certain threshold fluence the slow transient reflectivity component (neglecting the oscillatory part) changes to another value. This is associated with the switching to the H state and was described in details previously 3 .
To more accurately determine the states, we did fast Fourier transforms (FFT) of the data for the millisecond and picosecond states (at tD-P = -30 ps (corresponding to the relaxed state after 1 ms) and 30 ps, respectively), which are shown in Supplementary Figure 5. The maximum of the amplitude mode (AM) peak in the millisecond state stays approximately constant for the fluences of up to 3 mJ/cm 2 , and corresponds to the C state. Above that fluence the peak becomes broader and weaker, suggesting a change which does not relax back to the initial state within 1 ms. The data for the picosecond state shows a similar change above 3 mJ cm -2 as for the millisecond state, but the peaks are even more suppressed than for the millisecond state. The most important thing we see in the picosecond state is that at the fluences above 1 mJ cm -2 the AM peak shifts to lower frequencies, indicating the switching to the H state.
An equivalent set of measurements was done also at 160 K. The data shows the same characteristics as at 100 K. pulses. If the main mechanism is indeed heating, the sample should stay in the NC/triclinic state also after cooling and would not relax back to the C state at this temperature. In this case we would observe the characteristic oscillations of the triclinic or NC state when photoexciting the sample. Another thing that we could expect if heating was the transition mechanism, would be a decrease of the threshold fluence at higher temperatures. The highest measured fluences (up to 1.5 mJ/cm 2 ) are comparable or higher than the switching fluences observed at lower temperatures, but no change in the transient reflectivity is observed (Supplementary Figure 6). We conclude that switching to the H state is a different process than supercooling a thermodynamically stable state.  4 and thus a two pulse measurement of the C state was also made for the comparison. By exciting the sample with a 2.86 mJ/cm 2 laser pulse, the AM peak moves to a lower frequency with respect to the AM peak in the C state, consistently with observations at other temperatures. When observing the millisecond state, the AM peak seems to be a combination of both C and H AM peaks, suggesting that the sample is only partially relaxed. This is consistent with the STM measurements at 77 K, where the sample partially relaxes. By increasing the fluence to 4.41 mJ/cm 2 , we observe that the oscillations in the picosecond state have smaller amplitude consistently with the measurements at higher temperature. Fermi surface nesting is the dominant factor in determining the high temperature incommensurate charge density wave state 6 and could as such significantly influence the outcome of the model. On the other hand, our correlated polaronic approach is valid to a certain degree due to its ability to predict the many different states, which could arise in other similar systems 5 .