Hybridization Dynamics in ${\mathrm{CeCoIn}}_5$ Revealed by Ultrafast Optical Spectroscopy

We investigate the quasiparticle dynamics in the prototypical heavy fermion ${\mathrm{CeCoIn}}_5$ using ultrafast optical pump-probe spectroscopy. Our results indicate that this material system undergoes hybridization fluctuations before the establishment of heavy electron coherence, as the temperature decreases from $\sim 120\mathrm{K}$ ($T^{†}$) to $\sim 55\mathrm{K}$ ($T^{*}$). We reveal that the anomalous coherent phonon softening and damping reduction below $T^{*}$ are directly associated with the emergence of collective hybridization. We also discover a distinct collective mode with an energy of $\sim 8\mathrm{meV}$, which may be experimental evidence of the predicted unconventional density wave. Our findings provide important information for understanding the hybridization dynamics in heavy fermion systems.

Figure 1

(a) Typical $\mathrm{\Delta }R(t)/R$ as a function of temperature at a pump fluence of $\sim 0.45\mu \mathrm{J}/{\mathrm{cm}}^2$. (b) $\mathrm{\Delta }R(t)/R$ at 20 K as a function of the pump fluence. Relaxation below $\sim 2\mathrm{ps}$ shows strong fluence dependent. The relaxation can be fitted by a single exponential decay ($\propto e^{-\gamma t}$), where $\gamma$ is the decay rate. The fitting results below $\sim 2\mathrm{ps}$ are indicated by the solid lines with different colors. The green lines above $\sim 2\mathrm{ps}$ are guides to the eye. They are nearly the same except the shifting in $\mathrm{\Delta }R/R$ axis. (c) The decay rate $\gamma$ as a function of temperature measured at different fluences. Two clear anomalies at $T^{*}$ and $T^{†}$ are found ($T^{*}<T^{†}$). Below $T^{*}$, $\gamma$ shows strong fluence-dependent. Above $T^{†}$, $\gamma$ almost keeps constant.

Figure 2

(a) Illustration of the hybridization between local $f$ and conduction electrons below $T^{*}$, leading to the indirect gap, ${\mathrm{\Delta }}_{\mathrm{ind}}$, and the heavy fermion states near the Fermi energy $E_F$. (b) High energy excitations using 800 nm optical pulses in excess of ${\mathrm{\Delta }}_{\mathrm{ind}}$. Quasiparticles via high energy excitations decay to the gap edge via emission of high frequency phonons or other bosonic excitations. Subsequently, the bimolecular recombination dominates the decay and the relaxation rates become fluence dependent. (c) The density of thermally excited quasiparticles $n_T$ as a function of temperature below $T^{*}$. The inset shows the temperature dependence of the amplitude $A$. (d) Decay time ${\gamma }^{-1}$ as a function of temperature below $T^{*}$. The red lines are the fit using the RT model.

Figure 3

(a) Extracted oscillations for two typical temperatures: 15 and 290 K. Left panel includes the time-domain spectra, while the right is the corresponding fast Fourier transform (FFT) frequency-domain data. Additional FFT data for oscillation at 20 K is also shown for comparison. (b) Oscillation modes as functions of pump polarization and pump fluence at 5 K. Curves are shifted for clarity. The polarization is defined by the angle with respect to the original position (pump-probe cross polarized) after rotating anticlockwise. The fluence increasing step is $\sim 0.15\mu \mathrm{J}/{\mathrm{cm}}^2$.

Figure 4

The derived ${\omega }_2$ and ${\gamma }_2$ as a function of temperature using Eq. (2), where the red lines represent the fit using the anharmonic phonon model, while the blue and green lines are the fit taking into consideration the contribution of Kondo singlets with different $\alpha$, as described in the main text.