Revealing the role of electrons and phonons in the ultrafast recovery of charge density wave correlations in $\mathbf{1}T\text{−}{\mathbf{TiSe}}_{\mathbf{2}}$

Using time- and angle-resolved photoemission spectroscopy with selective near- and midinfrared photon excitations, we investigate the femtosecond dynamics of the charge density wave (CDW) phase in $1T\text{−}{\mathrm{TiSe}}_2$ as well as the dynamics of CDW fluctuations at 240 K. In the CDW phase, we observe the coherent oscillation of the CDW amplitude mode. At 240 K, we single out an ultrafast component in the recovery of the CDW correlations, which we explain as the manifestation of electron-hole correlations. Our momentum-resolved study of femtosecond electron dynamics supports a mechanism for the CDW phase resulting from the cooperation between the interband Coulomb interaction, the mechanism of excitonic insulator phase formation, and electron-phonon coupling.

Figure 1

(a) Schematic electronic band structure of $1T\text{−}{\mathrm{TiSe}}_2$ near the Fermi energy in the CDW phase ($T<T_c$), showing the original VB, the CB (continuous line), and the backfolded VB and CB in the CDW phase (dashed line). (b) and (c) Selected photoemission intensity maps in false color measured along $\overline{\mathrm{\Gamma }}\overline{M}$, near $\overline{M}$, and measured at different time delays, (b) before and (c) after the arrival of the MIR 3100-nm ($0.4\text{−}{\mathrm{mJ}/\mathrm{cm}}^2$) pump pulse in the CDW phase at 30 K. Guides to the eyes emphasize the relevant bands, and the position of $\overline{M}$ is given by the vertical dashed line. (d) Corresponding false color plots showing the intensity difference between the previous maps. (e) Schematic Fermi surface of $1T\text{−}{\mathrm{TiSe}}_2$ in the normal phase (no CDW) with one hole pocket at $\overline{\mathrm{\Gamma }}$ and three symmetry equivalent electron pockets at $\overline{M}$. (f) Energy distribution curves (EDCs) taken at $\overline{M}$ before time 0 (black curve) and at 50 fs (red curve). (f) Absolute value of the photoemission intensity changes integrated in the black boxes of graph (d) (the relative intensities of the curves have been scaled by the factors in the legend for better comparison).

Figure 2

(a) Photoemission intensity map in false color showing the photoemission intensity difference map taken at 30 K for MIR pump pulses [the same as in Fig. 1]. (b) Absolute value of the normalized photoemission intensity changes integrated in the black boxes of graph (a), together with the fit of the coherent phonon oscillation (total fit, green curve) and the exponential part of the fit only (dashed blue curve). (c) Schematic electronic structure of $1T\text{−}{\mathrm{TiSe}}_2$ in the CDW phase at $\overline{M}$. (d) Schematic of the displacements involved by the $A_{1g}$ coherent phonon excitation by the MIR pump pulse for a ${\mathrm{TiSe}}_6$ octahedron.

Figure 3

(a) Photoemission intensity map in false color showing the VB along $\overline{\mathrm{\Gamma }}\overline{K}$, near $\overline{\mathrm{\Gamma }}$, measured at 30 K before time 0 with a 1300-nm pump photon wavelength. (b) Corresponding false color plot showing the intensity difference induced by the pump pulse (positive and negative intensity changes in red and in blue, respectively) near $\overline{\mathrm{\Gamma }}$. Electrons and holes are excited resonantly at time 0 by the pump pulse, the energy of which is shown by the black arrow. (c) and (d) Corresponding intensity maps along $\overline{\mathrm{\Gamma }}\overline{M}$, near $\overline{\mathrm{\Gamma }}$ where part of the CB and the CDW band can be seen on the right side of the graphs. (e) Hexagonal Brillouin zone of $1T\text{−}{\mathrm{TiSe}}_2$ with the two directions relevant to graphs (a)–(d). (f) Photoemission intensity traces as a function of time delay integrated in the corresponding numbered black boxes on graphs (b) and (d). The curves are normalized to their maximum.

Figure 4

(a) Schematic electronic band structure of $1T\text{−}{\mathrm{TiSe}}_2$ near the Fermi energy in the normal phase ($T>T_c$), showing the original VB and CB (continuous line). (b) Selected photoemission intensity maps measured along $\overline{\mathrm{\Gamma }}\overline{M}$, near $\overline{M}$, and measured at different time delays before (left) and after (right) the arrival of the (NIR) 1300-nm ($0.5\text{−}{\mathrm{mJ}/\mathrm{cm}}^2$) pump pulse at 240 K (above $T_c$). Guides to the eyes emphasize the relevant CB, and the position of $\overline{M}$ is given by the vertical dashed line. (c) Corresponding false color plot showing the intensity difference between the previous maps. (d) Absolute value of the normalized photoemission intensity changes integrated in the black boxes of graph (c) with fits (lines) as guides to the eyes. (e) Transient photoemission intensity at the bottom of the CB at $\overline{M}$ [black box in the blue region of graph (c), at a binding energy (BE) of $-0.04\mathrm{eV}]$, together with the fitted slow (green) component (see the text). (f) Schematics of electron-electron scattering between the VB and the CB (blue arrows) and equivalently of electron-hole scattering (red arrows).

Figure 5

(a) False color plot of the transient photoemission intensity taken at 240 K [the same as in Fig. 4]. The blue arrows indicate the size of the pump photon energy (0.95 eV, 1300 nm) in comparison to the energy axis. (b) EDCs taken at $\overline{M}$ before time 0 (black curve) and at 130 fs (red curve). (c) Absolute value of the normalized photoemission intensity changes integrated in the black boxes of graph (a).

Figure 6

(a) EDCs taken at $\overline{M}$ at 240 K [integrated inside the dashed box of graph (c)] for different time delays. The dashed gray line is the reference EDC at $-600\mathrm{fs}$. (b) The same EDCs fitted by an exponential. (c) False color plot of the transient photoemission intensity at $\overline{M}$ [the same as in Fig. 4]. (d) Comparison of the electronic temperature with the fitted transient photoemission intensity at the bottom of the CB at $\overline{M}$ [black box in the blue region of Fig. 4] and the corresponding slow component fitted from the spectral feature (see the main text).