Energy-Gap Dynamics of Superconducting NbN Thin Films Studied by Time-Resolved Terahertz Spectroscopy

Using time-domain terahertz spectroscopy we performed direct studies of the photoinduced suppression and recovery of the superconducting gap in a conventional BCS superconductor NbN. Both processes are found to be strongly temperature and excitation density dependent. The analysis of the data with the established phenomenological Rothwarf-Taylor model enabled us to determine the bare quasiparticle recombination rate, the Cooper pair-breaking rate and the electron-phonon coupling constant, $\lambda =1.1\pm 0.1$, which is in excellent agreement with theoretical estimates.

Figure 1

The $T$ dependence of the (a) imaginary and (b) real part of $\sigma (\omega )$ of 15 nm NbN film on MgO substrate ($T_c=15.4\mathrm{K}$). Solid lines are fits with the BCS equations [29]. Inset to (a) shows the transmitted THz transients through the NbN film below and above $T_c$; the arrow denotes the time $t^{\prime }=t_0$ with maximum change in the transmitted electric field. Inset to (b): the $T$ dependence of $\Delta$, extracted from fits to $\sigma (\omega )$ (symbols) overlaying the normalized transmissivity ratio, TR. The BCS $T$ dependence of $\Delta$ is shown by the dashed line.

Figure 2

(a) The time evolution of normalized transmissivity ratio (TR), recorded at $A=22\mathrm{mJ}/{\mathrm{cm}}^3$, together with $\Delta (t)$ extracted from ${\sigma }_1(\omega ,t_d)$ fit with the BCS formula [29]. (b) Comparison of $\Delta (t_d)$ extracted from ${\sigma }_1(\omega ,t_d)$ (symbols) and from the spectrally integrated response $\Delta E_{\mathrm{tr}}(t_0,t_d)$ (dashed line). Inset: the measured $T$ dependence of $\Delta E_{\mathrm{tr}}(t_0)$ used to relate $\Delta E_{\mathrm{tr}}(t_0,t_d)$ to the change in $\Delta$.

Figure 3

(a) The relative change in gap, $\delta \Delta /{\Delta }_0$ recorded at 4.3 K for various $A$ in $\mathrm{mJ}/{\mathrm{cm}}^3$. The dashed lines are fits to the data with Eq. (1). (b) The dependence of $\delta \Delta /{\Delta }_0$ on $A$ at 4.3 K. The dashed line is a fit to the simple saturation model, the solid line is the linear fit. Inset: The $T$ dependence of the saturation energy density, $A_{\mathrm{sat}}$, compared to the $T$ dependence of ${\Delta }^2$ (dashed line).

Figure 4

Panels (a) and (b) show the dependence of $\tau /\beta$ and $K$ on $A$; the values are extracted from fits to the Cooper pair-breaking dynamics [Fig. 3a]. Panel (c) shows the $T$ dependence of the SC recovery time, ${\tau }_{\mathrm{rec}}$, for several $A$ (in $\mathrm{mJ}/{\mathrm{cm}}^3$). Inset: ${\tau }_{\mathrm{rec}}^{-1}(A)$ recorded at 4.3 K. For low $A$ the relaxation rate increases linear with $A$ (dashed line).