# Terahertz Photoconductive Antenna Based on a Topological Insulator Nanofilm
## 4 Discussion
By comparing the mean photocurrents detected in the TI antenna and the semiconductor PCA at the same bias voltage (Figure 5b), we obtained a ratio between the photocurrents (~1:7), which roughly corresponded to the ratio between the mobilities of bulk photoelectrons in both materials, \(\mu_{semi}=30~{}\text{cm}^{2}/(\text{V}\cdot\text{s})\) in our semiconductor InGaAs/InAlAs superlattice [33], and \(\mu_{TI}=166~{}\text{cm}^{2}/(\text{V}\cdot\text{s})\) in BSTS [36]. According to (3) this meant that the mean concentrations of photo-induced bulk electrons were the same in both materials. However, the peak-to-peak THz field amplitudes detected in TI and semiconductor PCAs (Figure 4a) refered to each other as 1.6:1. This indicates that the photocurrent change rate in BSTS was smaller than in the InGaAs/InAlAs superlattice. Thus, we estimated the ratio between the electron relaxation times in the both materials as \(\tau_{TI}/\tau_{semi}\sim(E_{\text{THz},semi}/E_{\text{THz},TI})(\mu_{TI}/ \mu_{semi})\sim 3.5\). Taking the previously measured value of the characteristic relaxation time for the InGaAs/InAlAs superlattice \(\tau_{semi}=1.7\) ps, we obtained the relaxation time for the bulk photo-induced electrons in BSTS as approximately \(\tau_{TI}\approx 6\) ps. Let us consider which relaxation process this time describes. In the case of BSTS, with extremely low initial concentration of free bulk carriers, the THz generation process began with the absorption of pump photons and the formation of electrons in the conduction band (Figure 7). The characteristic time of this process was of the order of the pump duration \(t_{0}\). Time \(t_{1}\) was of the order of a few picoseconds and, within this interval, a relaxation of bulk electrons took place due to the phonon emission [37]. The second type of relaxation process was an interband transition from the bulk conduction band to the surface states at the Dirac cone. As the Fermi level \(E_{f}\) lies in the band of surface states (SSs) in a BSTS with a composition near the Ren's curve, SSs above \(E_{f}\) were primarily unoccupied. The characteristic time \(t_{2}\) of this process is rather long, approximately 5-10 ps [37; 38]. Finally, the relaxation of SSs was the third relaxation mechanism, with time \(t_{3}\) as hundreds of femtoseconds or several picoseconds [9; 39]. The direct interband transitions from the conduction band to the valence band are rather long and usually last from hundreds to thousands of picoseconds. These slow processes do not significantly contribute to generation at THz frequencies. Our estimate of the relaxation time corresponds to \(t_{2}\). Thus, we concluded that the process of population of the edge states by photo-induced bulk electrons made up the main contribution to the formation of the THz generation spectrum of the BSTS TI PCA. The nonlinear \(\mathbf{j}_{NL}\) currents are known to appear in unbiased TIs due to photo-galvanic (PG) and photon-drag (PD) effects [10; 11; 12; 13; 14; 40; 41]. Currents induced in these processes should quadratically depend on the laser pump field, both under sub-bandgap excitation [40] and under above-bandgap [10; 13] laser excitation. Phenomenologically, dependences of these currents on the laser electric field for the non-stationary case [42] are described as:  
\[\mathbf{j}_{NL}^{PG}(t)=\int_{-\infty}^{t}\widehat{\beta}(t-t^{\prime},t-t^{ \prime\prime}):\mathbf{E}(t^{\prime})\mathbf{E}^{*}(t^{\prime\prime})dt^{ \prime}dt^{\prime\prime}+c.c., \tag{4}\]  
\[\mathbf{j}_{NL}^{PD}(t)=\int_{-\infty}^{t}\widehat{\gamma}(t-t^{\prime},t-t^{ \prime\prime}):\mathbf{E}(t^{\prime})\frac{\partial\mathbf{The PG effect takes place due to third-order tensor \(\widehat{\beta}(t-t^{\prime},t-t^{\prime\prime})\), which is non-zero only at the surface of TI. It is tied directly to the specific surface carriers, while both the bulk and surface electrons take part in PD effect via the fourth-order tensor \(\widehat{\gamma}(t-t^{\prime},t-t^{\prime\prime})\).