Ultrafast Electron Relaxation in Superconducting ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ by Time-Resolved Photoelectron Spectroscopy

Time-resolved photoelectron spectroscopy is employed to study the dynamics of photoexcited electrons in optimally doped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (Bi-2212). Hot electrons thermalize in less than 50 fs and dissipate their energy on two distinct time scales (110 fs and 2 ps). These are attributed to the generation and subsequent decay of nonequilibrium phonons, respectively. We conclude that 20% of the total lattice modes dominate the coupling strength and estimate the second momentum of the Eliashberg coupling function $\lambda {\Omega }_0^2=360\pm 30{\mathrm{meV}}^2$. For the typical phonon energy of copper-oxygen bonds (${\Omega }_0\simeq 40–70\mathrm{meV}$), this results in an average electron-phonon coupling $\lambda <0.25$.

Figure 1

(a) Sketch of the time-resolved ARPES experiment. An infrared pulse excites the sample while a delayed UV pulse generates the photoelectrons. (b) Photoelectrons intensity map acquired along the nodal direction (lattice temperature $T_l=30\mathrm{K}$). Vertical and horizontal bars display the energy and angular resolution, respectively. (c) Bonding and antibonding Fermi surfaces of Bi2212 in the reciprocal space. The arrow (red) marks the nodal vector $k_{\mathrm{F}}$.

Figure 2

(a) Time-resolved ARPES spectra acquired 200 fs before (black dots) and 100 fs after [gray (red) dots] the arrival of the pump pulse ($T_l=30\mathrm{K}$). (b) Time-resolved ARPES spectra acquired at $\tau =0\mathrm{fs}$ [gray (azure) line] and at $\tau =-200\mathrm{fs}$ (black line). Hypothetical spectrum of an electronic system that has fully thermalized at $T_e=770\mathrm{K}$ [dashed (violet) line]. (c) Logarithmic plot of the $k_{\mathrm{F}}$ spectrum collected at several pump-probe delays.

Figure 3

(a) The electronic temperature $T_e(\tau )$ is compared to the square root of the excess energy $\sqrt{E}(\tau )$. The function $\sqrt{E}$ is normalized to the maximum value. (b) Logarithmic plot of the electronic temperature ($T_l=30\mathrm{K}$). Three temporal windows indicate different cooling processes. The maximum increase of electronic temperature is marked by $\Delta T_e^{\alpha }$. Hot electrons and hot phonons converge to $T_l+\Delta T_e^{\beta }$ at $\tau =3{\tau }_{\alpha }=330\mathrm{fs}$. When $\tau >3{\tau }_{\beta }=6\mathrm{ps}$, the electrons and phonons reach local equilibrium. The solid line is the fitting result of the coupled Eqs. (1, 2, 3). (c) Sketch of the energy transfer during the relaxation process. Hot electrons generate hot phonons with characteristic time ${\tau }_{\alpha }$, while hot phonons dissipate their energy on a time scale ${\tau }_{\beta }\gg {\tau }_{\alpha }$.

Figure 4

Temporal evolution of electronic temperature for $T_l=30\mathrm{K}$ (black marks, left axis) and $T_l=300\mathrm{K}$ (red marks, right axis). The solid and dashed lines are numerical simulations of the hot electron and hot phonon temperature, respectively.