In order to confirm the cleaved surfaces of the sample and temperature-induced phase transitions, we perform the static ARPES measurements. Figure 2(a) shows the Fermi surface (FS) mapping of 1T-TaS2 measured at 240 K. The FS is clearly observed around the M point, which is indicated as a red oval. The photoemission intensity around the G point is ascribed to the flat band associated with the NCCDW phase [5]. Figures 2(b)-2(i) show the temperature-dependent ARPES images along the (b)-(e) G-M-G and (f)-(i) G-K-M directions. With decreasing temperature to 240 K, the flat band structure is more pronounced at the G point as a result of the band folding signifying the CDW phase [5]. With further decreasing temperature to 140 K, a small gap of the flat band with respect to EF is noticed, which corresponds to the Mott gap denoted as DMott[4]. Regarding the CDW phases, the ICCDW gap denoted as DICCDW around the M point increases with decreasing temperature. Besides, the two gaps associated with the CCDW phase denoted as DCCDW1/2 are observed at the band dispersion around the G point. The Mott and CDW gaps are more clearly seen in the enlarged ARPES image shown in Fig. 2(j), which corresponds to the white-dashed box region indicated in Fig. 2(i). These findings are consistent with the previous report [4].
Now we discuss the TARPES results. Figure 3(a) shows the TARPES image before the arrival of the pump pulse around the G point along the M-G-M direction. While the flat band is clearly observed, the CCDW gap at the band crossing point due to the CDW folding is not so clear due to the lack of energy resolution, which is typical for the HHG TARPES measurements. Just after the strong pump pulse excitation of 4.2 mJ/cm2, the system turns into the metallic phase [18]. Figure 3(b) shows the differential TARPES image at the delay time (Dt) of 240 fs. The increase and decrease of photoemission intensity are indicated as red and blue colors, respectively. It is noticed that the band dispersion crosses EF as the red region around EF increases. This demonstrates the photo-induced IMT with a collapse of the Mott gap as previously reported [18]. The complete set of TARPES images are shown in Fig. S1
[21]
. The transient electron temperature at 160 fs is estimated to be higher than 600 K as shown in Fig. S2 [21], which is above the NCCDW transition temperature (350 K), above which the flat band disappears in equilibrium.
To study the dynamics in more detail, Fig. 3(c) shows the time-dependent photoemission intensity integrated at the energy-momentum region denoted as I and II in Figs. 3(a) and 3(b). Overall, the immediate increase (decrease) at Dt = 0 ps followed by the fast decrease (increase) and slow relaxation is observed for the region I (II). Besides, significant oscillations are confirmed to be superimposed onto both data. Moreover, these oscillations have anti-phase character with respect to each other. For highlighting the oscillatory components, we first subtract overall dynamics by fitting to a double-exponential function convoluted with a Gaussian, shown as the black solid lines in Fig. 3(c). Fourier transformations are performed for the subtracted data, and amplitudes for each frequency component are shown in Fig. 3(d). One can see the strong single peak at 2.5 THz, which corresponds to the breathing A1g mode and is also called the CDW amplitude mode, confirmed by Raman spectroscopy [22], and the oscillation is as a result of coherent-phonon excitations based on the displacive excitation mechanism [23]. It should also be mentioned that the oscillation which appears in the TARPES measurements is due to the electron-phonon coupling, which connects the modulations between the lattice structure and electronic wave functions [24].
To further investigate the dynamical change of the electronic band dispersions modulated by the CDW amplitude mode, we proceed to FDARPES analysis. Figures 4(a) and 4(b) show the FDARPES images for amplitude and phase, respectively, at the frequency of 2.5 THz around the G point. FDARPES images at the different momentum cuts are shown in Fig. S3 [21]. One can notice that there exist two distinctive peak structures near and below EF shown as black squares and circles, respectively, in Fig. 4(a). Interestingly, their phases shown in Fig. 4(b) are different by nearly p, which was already seen as an anti-phase behavior in the time-dependent photoemission intensity in Fig. 3(c). This anti-phase character clearly shows that the single band oscillates between these two peak structures, synchronizing with the lattice modulation corresponding to the CDW amplitude mode, which is schematically shown in Fig. 5. The separation into the flat and M-shaped bands when the band shifts to the energetically lower position is due to the opening of the CDW gap, which is also seen at the temperature-dependent static ARPES shown in Fig. 2.
Strikingly, the shape of the band drastically changes between these two peak positions, and the flat band structure with a smaller Mott gap is clearly seen near EF shown as black squares in Fig. 4. As seen in the temperature-dependent static ARPES shown in Fig. 2, the flat band structure is the signature of the CDW phase. Based on this connection, the observed flat band in the FDARPES spectra strongly suggests that the CDW band folding survives even though the Mott phase is strongly suppressed seen as a collapse of the Mott gap. Furthermore, it is unveiled that the CDW amplitude mode can dynamically modulate the Mott gap corresponding to the position of the band dispersions with respect to the EF as well as the CDW gap corresponding to the distance between the flat and M-shaped band schematically seen in the blue circles in Fig. 5(b). These dynamical swinging between insulating and metallic phases related to the Mott and CDW phases are captured by FDARPES spectra. It is also of notice that these clear peaks are only elucidated in the frequency domain, never extracted in the time domain analysis as clearly noticed by seeing TARPES image in Fig. S2. The FDARPES technique relying on the lock-in amplification can greatly improve the signal-to-noise ratio by extracting only the relevant frequency component.