Ultrafast Formation of a Charge Density Wave State in $1T\text{−}{\mathrm{TaS}}_2$: Observation at Nanometer Scales Using Time-Resolved X-Ray Diffraction

Femtosecond time-resolved x-ray diffraction is used to study a photoinduced phase transition between two charge density wave (CDW) states in $1T\text{−}{\mathrm{TaS}}_2$, namely the nearly commensurate (NC) and the incommensurate (I) CDW states. Structural modulations associated with the NC-CDW order are found to disappear within 400 fs. The photoinduced I-CDW phase then develops through a nucleation and growth process which ends 100 ps after laser excitation. We demonstrate that the newly formed I-CDW phase is fragmented into several nanometric domains that are growing through a coarsening process. The coarsening dynamics is found to follow the universal Lifshitz-Allen-Cahn growth law, which describes the ordering kinetics in systems exhibiting a nonconservative order parameter.

Figure 1

(a) Crystal structure of $1T\text{−}{\mathrm{TaS}}_2$. The hexagonal unit cell is represented in red [18]. (b) Location of diffracted intensity in reciprocal space. Satellite peaks related to the $\overline{1}10$ lattice peak are represented in purple for the NC phase and in green for the I phase (filled circles: $l=\frac{1}{3}$, open circles: $l=-\frac{1}{3}$). Scanning the azimuthal angle $\phi$ allows measuring diffracted intensity along the thick red line.

Figure 2

(a) Diffracted intensity profiles measured at the NC and I satellite peak positions during the $\mathrm{NC}\to \mathrm{I}$ photoinduced phase transition of $1T\text{−}{\mathrm{TaS}}_2$ (absorbed fluence $6.8\mathrm{mJ}/{\mathrm{cm}}^2$, 265 K). The dots represent measured data and the solid lines their best fit using a pseudo-Voigt function. (b) Time dependence of the NC and I peak profile parameters, as extracted from the fit. (c) Schematic drawing of the three-step dynamics of the photoinduced $\mathrm{NC}\to \mathrm{I}$ phase transition. For each step, crystal views from both the top and the side are given.

Figure 3

(a) Time evolution of the normalized diffracted intensity at the NC satellite peak position $-1.313$, 1.245, 0.333 (240 K). Lines represent the best fits using a weighted sum of the model functions defined for regions 1 and 2 (see text). (b) Relative change of intensity observed for the NC satellite peak as a function of fluence ($\mathrm{\Delta }t=10\mathrm{ps}$). (c) Schematic representation of the inhomogeneous excitation across the probed depth of the $1T\text{−}{\mathrm{TaS}}_2$ crystal. The $z$ axis lies normal to the crystal’s surface.

Figure 4

(a) Diffraction profiles of the photoinduced I satellite peak ($F=6.8\mathrm{mJ}/{\mathrm{cm}}^2$, $T=240\mathrm{K}$). The strong contribution observed on the small angle side corresponds to the edge of the NC satellite peak. (b) Time evolutions of the integrated intensity of the I satellite peak (triangular dots), and of the photoinduced I-CDW correlation length (round dots).

Figure 5

(dots) Time evolution of the correlation length of the photoinduced I-CDW phase ($F=6.9\mathrm{mJ}/{\mathrm{cm}}^2$, $T=265\mathrm{K}$). (line) Best fit using the power law function $C\times \mathrm{\Delta }{t}^{0.5}$. The bottom right inset represents a subset of 3 I-CDW domains, each characterized by a different CDW phase ${\mathrm{\Phi }}_{\text{I}n}$. Modulations of electronic density associated with the I-CDW are color coded within each of the three domains. For the sake of simplicity, sharp domain walls are represented: their actual width cannot be deduced from the present experiment.