Temperature evolution of quasiparticle dispersion and dynamics in semimetallic $1T\text{−}{\mathrm{TiTe}}_2$ via high-resolution angle-resolved photoemission spectroscopy and ultrafast optical pump-probe spectroscopy

High-resolution angle-resolved photoemission spectroscopy and ultrafast optical pump-probe spectroscopy were used to study semimetallic $1T-{\mathrm{TiTe}}_2$ quasiparticle dispersion and dynamics. A kink and a flat band, having the same energy scale and temperature-dependent behaviors along the $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ direction, were detected. Both manifested at low temperatures but blurred as temperature increased. The kink was formed by an electron-phonon coupling. And the localized flat band might be closely related to an electron-phonon coupling. Ultrafast optical spectroscopy identified multiple distinct time scales in the 10–300 K range. Quantitative analysis of the fastest decay process evidenced a significant lifetime temperature dependence at high temperatures, while this starts to change slowly below $\sim 100$ K where an anomalous Hall coefficient occurred. At low temperature, a coherent $A_{1}g$ phonon mode with a frequency of $\sim 4.36$ THz was extracted. Frequency temperature dependence suggests that phonon hardening occurs as temperature falls and anharmonic effects can explain it. Frequency fluence dependence indicates that the phonons soften as fluence increases.

Figure 1

ARPES maps for the $1T\text{−}{\mathrm{TiTe}}_2$ Ti $3d$ band. (a1–a8) The band structure plots along the $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ direction at different temperatures. (b1–b8) Second-derivative images to enhance the weak bands corresponding to (a1–a8). The red and green arrows mark the kink and flat band, respectively.

Figure 2

(a) $\mathrm{\Delta }R/R$ as a function of delay time over temperature range from 10 to 300 K at a pump fluence of $\sim 25\mu \mathrm{J}/{\mathrm{cm}}^2$. (b) 2D pseudocolor map showing $\mathrm{\Delta }R/R$ as a function of temperature and delay times. (c) The blue line is a typical fitting of $\mathrm{\Delta }R/R$ at 180 K using four independent exponential decays. The inset shows four relaxation regions using different colors: Region 1 is the quickest relaxation process in $\sim 0.7$ ps. Region 2 shows a slower relaxation process between $\sim 0.7$ and $\sim 5$ ps. Region 3 shows a second rise occurring between $\sim 5$ and $\sim 17$ ps. Region 4 shows a very slow relaxation process lasting for more than 30 ps. (d), (e) The extracted lifetimes ${\tau }_1$, ${\tau }_2$, and ${\tau }_3$ as a function of temperature at two different fluences. ${\tau }_1$, ${\tau }_2$, and ${\tau }_3$ represent the relaxation processes 1, 2, and 3 indicated in the inset of (c), respectively. The inset of (d) displays ${\tau }_1$ as a function of the pump fluence for two different samples (S1 and S2).

Figure 3

Schematic band structure of semimetal $1T\text{−}{\mathrm{TiTe}}_2$ near the $E_F$ along the $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ direction. ${\tau }_1$, ${\tau }_2$, and ${\tau }_3$ represent $e\text{−}ph$ thermalization, phonon-assisted interband $e\text{−}h$ recombination, and reexcited $e\text{−}h$ pairs, respectively.

Figure 4

(a) Oscillations after subtracting nonoscillatory background at a pump fluence of $\sim 25\mu \mathrm{J}/{\mathrm{cm}}^2$ for four typical temperatures: 10, 80, 180, and 300 K. The fitted results are in red. (b) Fast Fourier transform (FFT) frequency-domain data corresponding to (a). Curves are shifted vertically for clarity. (c) The derived frequency $\omega /2\pi$ as a function of temperature at the two different fluences. The blue line is the fitted curve of the lower fluence data (red squares) using an anharmonic phonon model. (d) Pump fluence dependence of the frequency $\omega /2\pi$ at 10 K for two different samples (S1 and S2). The blue line serves as a guide for the eyes.