# Terahertz Photoconductive Antenna Based on a Topological Insulator Nanofilm
## 4 Discussion  
In general, a fairly large set of different mechanisms can be used to explain THz generation in TIs of double and quaternary compositions. The most instantaneous one is direct optical rectification of the laser pump field [11] due to nonlinear polarization. \[\mathbf{P}(t)\,\sim\int_{-\infty}^{t}\hat{\chi}^{(2)}(t-t^{\prime},t-t^{\prime \prime}):\mathbf{E}(t^{\prime})\mathbf{E}^{*}(t^{\prime\prime})dt^{\prime}dt^{ \prime\prime}+c.c. \tag{1}\]  
Here, \(\mathbf{E}(t)\) stands for the laser pump field and \(\hat{\chi}^{(2)}\) describes the second-order nonlinear-optical susceptibility. Due to the centrosymmetric structure of TI volume, the components of \(\hat{\chi}^{(2)}\) tensor are non-zero only at its surface and, thus, this effect is related specifically to surface excitations. However, its contribution was much smaller [34] than the THz field generated by transient currents of photo-induced charge carriers. The current-induced THz field depends on time derivatives of the two types of photocurrents, usually referred as linear (\(\mathbf{j}_{L}\)) and nonlinear (\(\mathbf{j}_{NL}\)) ones [15]:  
\[\mathbf{E}_{THz}(t)\,\sim\frac{\partial\mathbf{j}_{L}(t)}{\partial t}+\frac{ \partial\mathbf{j}_{NL}(t)}{\partial t}. \tag{2}\]  
In the frame of the simplest classical description, both types of currents should depend on temporal behaviour of the carrier's concentration \(N(t)\), mobility \(\mu\), and some specific field \(\mathbf{\tilde{E}}\) as:  
\[\mathbf{j}_{L,NL}(t)=e\mu N(t)\mathbf{\tilde{E}}. \tag{3}\]  
In our case of above-bandgap photo-excitation, the amplitude of the \(N(t)\) pulse scaled up with the pump pulse energy. As was reasonably argued in [35], the contribution from photo-induced electrons to both types of currents in BSTS was considerably more than the contribution from holes. A presence of non-zero dc field is necessary for directional motion of charge carriers in this description, regardless of whether it is applied externally or originates due to specific internal processes. The origin of, and the character of its possible temporal variation, are different for different THz generation mechanisms. In case of linear currents \(\mathbf{j}_{L}\), the temporal variation of \(\mathbf{\tilde{E}}\) was negligible. In a photoconductive antenna, \(\mathbf{\tilde{E}}=\mathbf{E}_{dc}\) is created by an external bias voltage source. With significantly smaller magnitudes, \(\mathbf{\tilde{E}}\) also exists as a surface depletion field or due to the photo-Dember effect [15], regardless of whether an additional lateral external field is applied. The surface depletion and photo-Dember fields are directed along the normal to the TI surface and determine the motion of volume carriers even in case of zero applied voltage. In addition, some surface built-in field can exist in the lateral direction and be responsible for the specific contribution of surface carriers to THz generation. For all generation effects caused by different-type linear currents, the THz waveforms should have almost the same shape,  
Figure 6: The (**a**) THz pulses at opposite bias voltages; and (**b**) comparison of the unbiased THz pulse (blue) with the result of averaging of two waveforms from oppositely biased antennas (magenta). repeating the shape of \(\partial N(t)/\partial t\). This shape is clearly presented in waveforms like those in Figure 6a. The waveforms were obtained in the case where the high external bias field made \(\mathbf{j}_{L}\) more than other nonlinear contributions to the net photo-induced current. It was seen that changing the bias voltage sign did not cause any observable changes in the THz field magnitude, apart from reversing its sign. Moreover, both curves in Figure 6b demonstrate the zero residual THz field at delay times, when contribution of linear currents should be maximal. Thus, we concluded that the effects of lateral and longitudinal built-in fields were negligible at zero voltage, and were not linearly enhanced when the bias voltage was applied to the TI antenna.