Spatially resolved femtosecond pump-probe study of topological insulator Bi${}_2$Se${}_3$

Carrier and phonon dynamics in Bi${}_2$Se${}_3$ crystals are studied by a spatially resolved ultrafast pump-probe technique. Pronounced oscillations in differential reflection are observed with two distinct frequencies and are attributed to coherent optical and acoustic phonons, respectively. The rising time of the signal indicates that the thermalization and energy relaxation of hot carriers are both sub-ps in this material. We found that the thermalization and relaxation time decreases with the carrier density. The expansion of the differential reflection profile allows us to estimate an ambipolar carrier diffusion coefficient on the order of 500 cm${}^2$/s. A long-term slow expansion of the profile shows a thermal diffusion coefficient of 1.2 cm${}^2$/s.

Figure 1

Panel (a) shows schematically the experimental system used for the experiment. Panel (b) shows the spatial profiles of the differential reflection signal measured by scanning the probe spot in the $x-y$ plane with a probe delay of 0.4 ps. The peak energy fluence of the pump pulse is 56 $\mu$J/cm${}^2$. Panel (c) shows a cross section on the $x$ axis ($y=0$).

Figure 2

Panel (a) shows the differential reflection signal as a function of the probe delay and $x$, measured with $y=0$. Panel (b) shows the peak differential reflection signal ($x=y=0$) as a function of the probe delay (solid line, right axis). The squares (left axis) show the width (FHWM) of the profile as a function of probe delay, obtained through a procedure shown in Fig. 3.

Figure 3

Panel (a) shows the spatial profile of differential reflection with a probe delay of 0.35 ps (red/highest) and with negative delays (gray/lowest). The blue/middle curve is the difference. Panel (b) shows the profiles (after removing the background) measured at probe delays of (from wide to thin) 1.78 (red), 0.35 (black), 15.8 (blue), and 10.7 ps (pink), respectively. Panel (c) is the same as Fig. 2b but with a smaller time range near zero delay. The gray area shows the cross correlation of the pump and the probe pulses.

Figure 4

Panel (a) shows the peak differential reflection signal ($x=y=0$) as a function of the probe delay with different pump fluences, as indicated in each plot. Panels (b) and (c) summarize the characteristic times and the peak of the signal as functions of the pump fluence.

Figure 5

Panel (a) shows the peak differential reflection signal ($x=y0$) as a function of the probe delay in the first 8 ps, with the pump fluences of (from bottom to top) 0.6, 1.1, 2.2, 3.4, 4.5, 5.6, 7.8, 11.2, 16.8, 22.4, 28, 33.6, 39.2, 44.8, and 50.4 $\mu$J/cm${}^2$. The inset shows the high-frequency oscillation obtained by using a high-pass filter with a cutoff frequency of 2 THz. Panel (b) summarizes the initial amplitude (squares), the frequency (circles), and the decay time (triangles) that are obtained from the fits.

Figure 6

The peak differential reflection signal ($x=y=0$) as a function of the probe delay with different pump spot sizes of 3 $\mu$m (blue/lower) and 11 $\mu$m (red/upper), respectively. The energy fluence of the pump pulse at the center of the spots is 17 $\mu$J/cm${}^2$ for both measurements. The inset shows the two curves at early probe delays.