In recent years, significant attention has been paid to the nonlinear response of Weyl semimetals, in which either the inversion or time-reversal symmetry is broken. For example, it was confirmed that the second-order optical responses in the type-I Weyl semimetal TaAs, including the shift and injection current and second-harmonic generation (SHG), relate to the topological effects of Weyl semimetals. Remarkably, Dirac or Weyl semimetals have been proposed to support divergently large current-induced SHG when the Fermi level is located near the Dirac/Weyl points. Such current-induced SHG components have been demonstrated in TaAs using an optically pumped shift current. Compared to the optical pump, the terahertz (THz) pump is advantageous because extremely strong THz fields such as 1‒80 MV/cm can be applied without a significant heating effect. In this study, we used the intense THz generated by the tilted wavefront method as the pump beam and the SHG probe to explore the TaAs third-order nonlinear response.
A Ti sapphire femtosecond laser amplifier generates 35 fs pulses with a central wavelength of 800 nm, repetition rate of 1 kHz, and single-pulse energy of 7 mJ. 95% laser energy was employed to generate THz radiation from a MgO-doped LiNbO3 crystal (doping concentration of MgO is 5%) using tilted wavefront technique. The THz radiation generated with 0.8 THz center frequency (pump beam) was focused on the sample surface using three off-axis parabolic mirrors. A pair of wire-grid polarizers was used to attenuate the THz field and change polarization. The remaining weak laser pulse (probe beam) was used to generate SHG from the sample. The probe pulses were focused on the sample surface through a hole in the last off-axis parabolic mirror at near-normal incidence. Polarization of the probe pulses was rotated using a half-wave plate. The SHG signal generated at approximately 400 nm was delivered through several bandpass filters and detected using a photomultiplier tube. The SHG polarization was filtered using a wideband wire-grid polarizer mounted on a motorized stage. High-quality single crystals TaAs were grown via a chemical vapor transport method using iodine as the agent.
The maximum pulse energy of THz radiation at the sample position was 6.4 μJ, measured by a commercial thermopile detector (Ophir, 3A-P-THz). The size of the focused THz spot was measured using an uncooled microbolometer THz camera (Swiss Terahertz, S2x). Assuming a Gaussian beam profile, a focus diameter of 530 and 600 μm at the sample position was obtained (Fig. 3). The THz electric field intensity was estimated to be 970 kV/cm at the peak from electro-optic sampling measurements. First, we determined the orientation of the high-symmetry axes on the (112) surface of the TaAs crystal using the static SHG pattern (Fig. 4). With the arrival of the pump pulse, the time-resolved THz field-induced SHG (TFISHG) signal followed the temporal profile of the pump THz pulse. The peak value of the TFISHG signal increases linearly with an increase in the THz electric field intensity (Fig. 5), which is probably owing to the existence of a large TaAs second-order susceptibility tensor. The TFISHG pattern was collected when the strong-field THz radiation was selectively pumped along the two in-plane [1,-1,0] and [1,1,-1] axes of the (112) face. The TFISHG signal was two orders of magnitude smaller than the static SHG signal, albeit exhibited a clear dependence on the THz electric field direction (Fig. 6). These results can be explained quantitatively by third-order nonlinear polarization introduced by the pump THz electric field. We analyzed the mathematical forms of the third-order susceptibility tensor and discussed the possibility of an exotic topological origin for certain components of this tensor. Finally, we briefly commented on the difference in the transient SHG signals induced by femtosecond laser and strong-electric-field THz pulses.
In summary, we report the measurements of the third-order nonlinear optical response in Weyl semimetal TaAs crystals driven by an intensity THz beam with a peak electric field intensity of 970 kV/cm. The TFISHG signal exhibited different polarization dependencies when the pumps THz electric field was along the two special axes of the TaAs (112) surface. The TFISHG signal can be quantitatively explained by third-order nonlinear polarization introduced by the THz electric field, where the topological nontrivial zzzz component may play a crucial role. Our results suggest that strong electric field terahertz can be applied to alter the symmetry of topological material on ultrafast time scale, thus providing the possibility to further control the topological properties that are associated with symmetry.
