Robust hybridization gap in the Kondo insulator $\mathrm{Yb}{\mathrm{B}}_{12}$ probed by femtosecond optical spectroscopy

In heavy fermions the relaxation dynamics of photoexcited carriers has been found to be governed by the low energy indirect gap ${\mathrm{E}}_g$ resulting from hybridization between localized moments and conduction band electrons. Here, carrier relaxation dynamics in a prototype Kondo insulator $\mathrm{Yb}{\mathrm{B}}_{12}$ is studied over a large range of temperatures and over three orders of magnitude. We utilize the intrinsic nonlinearity of dynamics to quantitatively determine microscopic parameters, such as electron-hole recombination rate. The extracted value reveals that hybridization is accompanied by a strong charge transfer from localized $4f$ levels. The results imply the presence of a hybridization gap up to temperatures of the order of ${\mathrm{E}}_g/{\mathrm{k}}_B\approx 200$ K, which is extremely robust against electronic excitation. Finally, below 20 K the data reveal changes in the low energy electronic structure, attributed to short-range antiferromagnetic correlations between the localized levels.

Figure 1

Dynamics of photoinduced change in reflectivity of the $\mathrm{Yb}{\mathrm{B}}_{12}$ single crystal at 800 nm. (a) Dynamics recorded at 5 K base temperature as a function of $F$ over three orders of magnitude. All traces were normalized to $F$. (b) $T$ dependence of reflectivity traces recorded at $F=8\mu \mathrm{J}/{\mathrm{cm}}^2$. Dashed lines are fits to the data (see text). Note the break in the $x$ axis. Continuous laser heating is less than 1 K over the entire range of temperatures and excitation densities.

Figure 2

$T$ dependence of (a) thermally excited EHP density extracted from the $T$ dependence of $A_1$, presented in the inset, and (b) the relaxation rate $\gamma$. The data were recorded at $F=8\mu \mathrm{J}/{\mathrm{cm}}^2$. The solid spheres are the experimental data and the dotted lines are fits to the data (see text).

Figure 3

The analysis of the $F$ dependence of transient reflectivity at 5 K using the phonon-bottleneck model [20]. Panel (a) presents the data recorded for $F$ spanning three orders of magnitude (solid lines) fit by the global fit (dashed lines), providing access to parameters $R, \beta$, and $r$. (b) The $F$ dependence of reflectivity change at 15 ps time delay (open black squares), together with the fit (dashed line) with ${\mathrm{n}}_s(F$), given by Eq. (4). Inset presents the same data on the linear scale. (c) The $F$ dependence of the relaxation rate $\gamma$ (open blue circles), fit by $\gamma \propto (n_s+E)$ (dashed line). For all fits the same values of microscopic parameters were used: $\mathrm{r}=0.47+/-0.01, \beta =0.61+/-0.01{\mathrm{ps}}^{-1}$, and $\mathrm{R}=0.14+/-0.01{\mathrm{ps}}^{-1}\mathrm{ucv}$.

Figure 4

Simulation of early stage QP dynamics in the absence of the decay channel (which proceeds via phonon escape/anharmonic decay). Panel (a) presents the evolution for constant $F=1$ mJ/${\mathrm{cm}}^2$ and different values of $r$ from 1 (all the energy initially in the QP channel) to 0 (all the energy initially in the HFP channel). (b) Fluence dependence of dynamics for constant $R, b, r$ (the values are given in the plot). Here $n\left(t\right)$ is normalized to excitation fluence $F$ to emphasize the nonlinearity of dynamics.