Higgs Amplitude Mode in the BCS Superconductors ${\mathrm{Nb}}_{1\mathrm{\text{−}}x}{\mathrm{Ti}}_x\mathbf{N}$ Induced by Terahertz Pulse Excitation

Ultrafast responses of BCS superconductor ${\mathrm{Nb}}_{1\mathrm{\text{−}}x}{\mathrm{Ti}}_x\mathrm{N}$ films in a nonadiabatic excitation regime were investigated by using terahertz (THz) pump-THz probe spectroscopy. After an instantaneous excitation with the monocycle THz pump pulse, a transient oscillation emerges in the electromagnetic response in the BCS gap energy region. The oscillation frequency coincides with the asymptotic value of the BCS gap energy, indicating the appearance of the theoretically anticipated collective amplitude mode of the order parameter, namely the Higgs amplitude mode. Our result opens a new pathway to the ultrafast manipulation of the superconducting order parameter by optical means.

Figure 1

(a) A schematic picture of the phase and amplitude modes represented by the arrows in azimuthal and radial directions, respectively, on the effective potential in the plane of complex order parameter $\Psi$. (b) Schematic configuration of the TPTP spectroscopy. WGP: a wire grid polarizer. (c) Temperature dependence of the real-part optical conductivity spectra in sample C without the pump. The solid curves are calculated by the Mattis-Bardeen model. (d) Temperature dependences of the BCS gap energies for samples A, B, and C. (e) The waveforms of the probe THz $E$ field $E_{\mathrm{probe}}$ as a function of the gate delay time $t_{\mathrm{gate}}$ at various temperatures without the pump. (f) The temperature dependence of the BCS gap $2\Delta$ in equilibrium and $E_{\mathrm{probe}}$ at the fixed delay time of $t_{\mathrm{gate}}=2.1\mathrm{ps}(=t_0)$ indicated by the vertical line in (e) for sample A.

Figure 2

(a) The open circles show the temporal evolution of the change of the probe $E$ field, $\delta E_{\mathrm{probe}}$, at $t_{\mathrm{gate}}=t_0$ as a function of $t_{\mathrm{pp}}$ in sample A at 4 K. The solid curves show the fitted results with Eq. (1). (b) The oscillation frequency $f$ obtained from the fits and the asymptotic gap energy $2{\Delta }_{\infty }$ as a function of the pump intensity. (c) The power-law decay index $b$ as a function of the pump intensity.

Figure 3

(a) The temporal evolution of the real-part optical conductivity spectra ${\sigma }_1(\omega )$ with the peak $E$ field of $10\mathrm{kV}/\mathrm{cm}$ of the pump THz pulse at 4 K as functions of the frequency and $t_{pp}$. (b) ${\sigma }_1(\omega )$ spectra at each $t_{\mathrm{pp}}$ indicated by the dotted lines in (a). The dotted curves show the spectrum before the pump ($t_{\mathrm{pp}}=-2\mathrm{ps}$). The arrows are guides for the eyes to the oscillation.

Figure 4

(a),(b) The temporal evolution of $\delta E_{\mathrm{probe}}$ at a fixed delay $t_{\mathrm{gate}}=t_0$ as a function of $t_{\mathrm{pp}}$ in samples B and C at 4 K, respectively, for various pump intensities. The regions surrounded by the dotted lines are enlarged in the insets with the fitted curves and the oscillation frequencies.