Real-Time Observation of Phonon-Mediated $\sigma \text{−}\pi$ Interband Scattering in ${\mathrm{MgB}}_2$

In systems having an anisotropic electronic structure, such as the layered materials graphite, graphene, and cuprates, impulsive light excitation can coherently stimulate specific bosonic modes, with exotic consequences for the emergent electronic properties. Here we show that the population of $E_{2g}$ phonons in the multiband superconductor ${\mathrm{MgB}}_2$ can be selectively enhanced by femtosecond laser pulses, leading to a transient control of the number of carriers in the $\sigma$-electronic subsystem. The nonequilibrium evolution of the material optical constants is followed in the spectral region sensitive to both the $a$- and $c$-axis plasma frequencies and modeled theoretically, revealing the details of the $\sigma \text{−}\pi$ interband scattering mechanism in ${\mathrm{MgB}}_2$.

Figure 1

(a) Color-coded map of $\mathrm{\Delta }R/R$ at 10 K as a function of probe photon energy and time delay between pump and probe. The pump photon energy is 1.55 eV and the absorbed fluence is $1.2\mathrm{mJ}/{\mathrm{cm}}^2$. (b), (c) Transient spectra of $\mathrm{\Delta }R/R$ for different time delays during (b) the rise and (c) the decay of the response. (d) Time evolution of the $P_c$ peak energy.

Figure 2

(a) Normalized $\mathrm{\Delta }R/R$ temporal traces up to 2.5 ps at 10 K for different probe photon energies, indicated in the labels. (b) $\mathrm{\Delta }R/R$ temporal traces up to 12 ps in correspondence of the $P_a$ and $P_c$ spectral features.

Figure 3

Temporal evolution of (a) the bare plasma frequency ${\omega }_{p,a/c}$ and (b) the optical scattering rate ${\mathrm{\Gamma }}_{a/c}$ along the $a$ axis (purple dots) and the $c$ axis (blue dots). (c) Illustration of the ultrafast dynamics. After the interaction with the solid, the ultrashort laser pulse leads to the excitation of both $\sigma$ and $\pi$ carriers. The nonthermal $\sigma$ carriers are strongly coupled to the branch of the $E_{2g}$ phonon mode and efficiently generate hot phonons during the first 170 fs. Subsequently, the energy stored in the hot phonon subsystem is released to the $\pi$ carriers via interband scattering and to low-energy phonons via anharmonic decay.