Picosecond Trajectory of Two-dimensional Vortex Motion in FeSe${}_{0.5}$Te${}_{0.5}$ Visualized by Terahertz Second Harmonic Generation

We have investigated the vortex dynamics in a thin film of an iron-based superconductor FeSe${}_{0.5}$Te${}_{0.5}$ by observing second-harmonic generation (SHG) in the THz frequency range. We visualized the picosecond trajectory of two-dimensional vortex motion in a pinning potential tilted by Meissner shielding current. The SHG perpendicular to the driving field is observed, corresponding to the nonreciprocal nonlinear Hall effect under the current-induced inversion symmetry breaking, whereas the linear Hall effect is negligible. The estimated vortex mass, as light as a bare electron, suggests that the vortex core moves independently from quasiparticles at such a high frequency and large velocity $\approx$300 km/s.