Strong Terahertz Third-Harmonic Generation by Kinetic Heavy Quasiparticles in ${\mathrm{CaRuO}}_3$

We report on time-resolved nonlinear terahertz spectroscopy of a strongly correlated ruthenate, ${\mathrm{CaRuO}}_3$, as a function of temperature, frequency, and terahertz field strength. Third-harmonic radiation for frequencies up to 2.1 THz is observed evidently at low temperatures below 80 K, where the low-frequency linear dynamical response deviates from the Drude model and a coherent heavy quasiparticle band emerges by strong correlations associated with the Hund’s coupling. Phenomenologically, by taking an experimentally observed frequency-dependent scattering rate, the deviation of the field driven kinetics from the Drude behavior is reconciled in a time-dependent Boltzmann description, which allows an attribution of the observed third-harmonic generation to the terahertz field driven nonlinear kinetics of the heavy quasiparticles.

Figure 1

(a) Illustration of the THz THG experiment. THG from ${\mathrm{CaRuO}}_3$ thin film is measured in transmission configuration and the THz electric field is detected by electro-optic sampling (EOS). (b) Electric field of the THz pump pulse with a central frequency of $f=0.5\mathrm{THz}$. (c) THz electric field emitted from ${\mathrm{CaRuO}}_3$ at 5 K measured through a $3f$-bandpass (BP) filter. (d) Spectrum obtained by Fourier transformation of the waveform in panel (c). (e) THG amplitude $E_{3f}$ vs driving field amplitude $E_f$, which follows a power law dependence of $E_{3f}\propto E_f^{2.6}$ (solid line) only slightly deviated from the perturbative dependence $\propto E_f^3$ (dashed line).

Figure 2

(a) THG signal in time domain at different temperatures. (b) Fourier amplitude of the signal in panel (a). (c) THG amplitude $E_{3f}$ and (d) the transmitted amplitude $E_f$ of the fundamental frequency as a function of temperature.

Figure 3

(a) Experimentally determined $|{\chi }^{(3)}|\propto (E_{3f}/E_f^3)$ as a function of temperature for driving frequencies of 0.4, 0.5, and 0.7 THz. (b) Normalized $|{\chi }^{(3)}|$ for THz drive frequencies of $f=0.4$, 0.5, and 0.7 THz follow the same temperature dependence. The shaded area represents the simulated $|{\chi }^{(3)}|$ where the width reflects the uncertainties of experimentally determined $\alpha$ in (c) [7]. (d) Simulated spectral amplitude of emitted electric field for $\alpha =0$ and $\alpha <0$ at 5 K versus harmonic order. (e) Snapshots of charge-carrier distribution $f(p)$ at zero and peak THz electric field $E_{\max }$ at 5 K. (f) Changes of charge-carrier distribution at $E_{\max }$ for different experimental values of $\alpha$ with respect to that of $\alpha =0$.