Observation of soft Leggett mode in superconducting ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$

We study the ultrafast dynamics of the multiband iron-based superconductor ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ via time-resolved optical reflectivity. We observe a long-lived 5- GHz oscillation of the reflection changes within the superconducting regime. We assign this low-frequency oscillation to a soft Leggett mode associated with the collective fluctuation of multiple phase differences between Cooper pair condensates. Our observation evidences the presence of the time-reversal-symmetry breaking state in superconducting ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$.

Figure 1

Transient reflectivity changes $\mathrm{\Delta }R/R$ as a function of temperature for a fixed pump fluence $F$ = 120 $\mu \mathrm{J}/{\mathrm{cm}}^2$. The results in the picosecond regime $t<50\mathrm{ps}$ and in the subnanosecond regime $t>50\mathrm{ps}$ are presented in different time scales. The inset shows normalized $\mathrm{\Delta }R/R$ curves. The black curve represents a triexponential fit of the picosecond signals yielding three characteristic times ${\tau }_{1,2,3}$. The subnanosecond result is further analyzed in Figs. 2, 3, 4.

Figure 2

Superconductivity-enhanced amplitudes $|\mathrm{\Delta }R/R(T)-\mathrm{\Delta }R/R(40\mathrm{K}\left)\right|$ as a function of temperature at $\sim 0$ (the sharp dip), 15, and 50 ps extracted from Fig. 1. The black curve represents the fit of the result at 15 ps based on Eq. (3), yielding the zero-temperature gap $\mathrm{\Delta }\left(0\right)$ = 10 $\pm$ 1 meV.

Figure 3

Characteristics of coherent oscillations as a function of pump fluence. (a) Subnanosecond $\mathrm{\Delta }R/R$ signals for various fluences from 6 to 240 $\mu \mathrm{J}/{\mathrm{cm}}^2$ at $T=5$, 20, 30, and 50 K. (b) Coherent oscillations ${(\mathrm{\Delta }R/R)}_L$ extracted from the result in (a) by subtracting the exponential decay of each curve according to Eq. (3). (c) FFT curves of the result in (b). (d) FFT peak intensity versus the pump fluence. The gray line is used to guide the eye for a linear relation.

Figure 4

Characteristics of coherent oscillations as a function of temperature. (a) ${(\mathrm{\Delta }R/R)}_L$ signals from 5 to 50 K for fluences 120 and $180\mu \mathrm{J}/{\mathrm{cm}}^2$. The black curves depict the fits of the lower fluence signals by using Eq. (5). (b) Nomalized FFT amplitude of the lower fluence signals (the red curve). The oscillation mode becomes invisible for $T>T_{\nu }\approx 29\mathrm{K}$. We show the SC transition $T_c\approx 35\mathrm{K}$ signals (the blue curve) obtained by a magnetic measurement (Zero-field cooled and $H=10\mathrm{Oe}$). (c) and (d) Frequencies ${\nu }_{\mathrm{L}}, {\omega }_{\mathrm{L},0}$ and damping time ${\tau }_{\mathrm{D}}$ and initial amplitude $\mathcal{B}$ as functions of temperature, respectively, extracted from (a).