Polarization dependence of coherent phonon generation and detection in the three-dimensional topological insulator $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$

We have studied the polarization dependence of coherent phonons in the topological insulator $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$. Using polarization-dependent femtosecond pump-probe spectroscopy, we measured coherent phonons as a function of angle when the pump and probe polarizations were fixed, and the crystal orientation was rotated. For isotropic detection, depending on the spot position, oscillations either from only low- and high-frequency phonons of $A_{1g}$ symmetry, or in addition from the mode at 3.6 THz were observed. All the modes were found to be independent of the orientation of electric field vector with respect to the crystal axes testifying to their full symmetry while no modes of lower symmetry appeared in any polarization geometry. For anisotropic detection both modes of $E_g$ symmetry could be detected, but their amplitudes were considerably smaller than those of $A_{1g}$ symmetry. To clarify the coherent phonon assignment and the process of coherent phonon generation in $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$, the time-domain measurements were complemented by spontaneous Raman scattering. The comparison of frequency- and time-domain results and the polarization dependence suggest that the 3.6 THz mode belongs to crystalline Te arising due to tellurium segregation. A discrepancy between the time- and frequency-domain data is discussed.

Figure 1

The atomic displacements in Raman active modes of $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$ according to a factor group analysis. The small blue and the large red circles denote Te and Bi atoms, respectively.

Figure 2

A typical differential change in reflection in $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$ showing $A_{1g}$ coherent oscillations (a) and its fast FT spectrum (b). The inset in (a) shows the full trace measured out to long delay times. The open symbols in (b) are experimental points, while the solid red lines are the Fano fits ($q=6.8$ and $\mathrm{\Gamma }=0.22$ for the high-frequency mode; $q=5.5$ and $\mathrm{\Gamma }=0.08$ for the low-frequency mode).

Figure 3

A typical differential change in reflection in $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$ showing $A_{1g}$ coherent oscillations (a) and its derivative to separate the coherent part (b). In (b) circles are experimental points, whereas red solid line is the fit to two damped harmonic oscillators, see text.

Figure 4

FT spectra of the data in Fig. 2 when left positions of the time window for FT are shifted. Legends show different values of positions used. Data were normalized to the amplitude of the low frequency mode.

Figure 5

Coherent phonon amplitudes of different modes obtained from the fast FT spectra as a function of angle. Legends specify the modes. The data were normalized to the amplitude of low-frequency $A_{1g}^{\left(\mathrm{I}\right)}$ mode and the dashed lines are a guide to the eye.

Figure 6

Differential change in reflection in $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$ showing coherent oscillations (a) and its fast FT spectrum (b). The open symbols in (b) are experimental points, the solid line is a cumulative fit to three Lorentzian profiles.

Figure 7

Differential change in reflection for (0001) Te single crystal showing (a) $A_1$ coherent oscillations and (b) its fast FT spectrum.

Figure 8

Raman spectra of $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$ in backscattering geometry with an electric field parallel to the long dimension of the crystal (laser power at the sample position $-0.8\mathrm{mW}$). The open symbols are experimental points, the solid lines are a cumulative fit to Lorentzian profiles. The upper trace is the polarized spectrum and the lower trace is the depolarized spectrum. Both the incident and scattered light polarizations belong to $xy$ plane. The spectra are vertically offset for clarity.

Figure 9

Typical unpolarized Raman spectrum (open symbols) of $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$ in backscattering geometry without using analyzer showing additional lines (laser power at the sample position $-4\mathrm{mW}$). For comparison purposes, unpolarized spectrum of (0001) Te is also shown by a red solid line (laser power at the sample position $-0.7\mathrm{mW}$). Both spectra were normalized relative to the intensity of the strongest mode.

Figure 10

Differential change in reflection in damaged $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$ showing (a) coherent oscillations and (b) its fast FT spectrum.

Figure 11

Typical isotropic (upper trace) and anisotropic (lower trace) change in reflection for $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$ showing (a) coherent oscillations and (b) their normalized fast FT spectra. The two lower spectra obtained with anisotropic detection differ from each other by the angle between the pump polarization and crystal axis, 0 (solid line) and π/4 (dashed line), respectively. The traces and spectra are vertically offset for clarity.