Momentum-Resolved Ultrafast Electron Dynamics in Superconducting ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathbf{O}}_{8+\delta }$

The nonequilibrium state of the high-$T_c$ superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ and its ultrafast dynamics have been investigated by femtosecond time- and angle-resolved photoemission spectroscopy well below the critical temperature. We probe optically excited quasiparticles at different electron momenta along the Fermi surface and detect metastable quasiparticles near the antinode, since their decay toward the nodal region through $e\mathrm{\text{−}}e$ scattering is blocked by phase space restrictions. The observed lack of momentum dependence in the decay rates is in agreement with relaxation dynamics dominated by Cooper pair recombination in a boson bottleneck limit.

Figure 1

(a) Sketch of the normal state FS of Bi-2212. Circles mark the FS angles, $\varphi =18°$, 27°, 37° and 45°, considered in this work. Some of the arcs cutting the FS along which the ARPES spectra were taken are also shown. (b) ARPES spectra and their representation as a false color plot, measured along the red arc in (a). The spectra measured at the FS ($\varphi =27°$ and 63°) are highlighted with red thick lines in the lower panel. (c) ARPES spectra measured at $\varphi =18°$ as a function of the temperature. The intensity of every spectrum has been normalized to its value at $-0.15\mathrm{eV}$.

Figure 2

(a) trARPES spectra measured at several pump-probe delays. The depletion of the superconducting peak and the increase of spectral weight above the Fermi level, in relation to the spectrum measured before optical excitation, are shadowed in yellow (bright) and gray (dark), respectively. (b) Depletion of the superconducting peak [yellow (bright) area between the vertical gray lines in (a)] and increase of the intensity above the Fermi level [gray (dark) area in (a)] as a function of the pump-probe delay.

Figure 3

Relative trARPES intensity change above $E_F$, $\Delta I/I$, measured at different FS angles, $\varphi$, using a pump fluence $F=32\mu \mathrm{J}/{\mathrm{cm}}^2$ (a) and measured at $\varphi =27°$, using different pump fluences (b). A zoom of the spectra measured at $\varphi =27°$ with $F=139\mu \mathrm{J}/{\mathrm{cm}}^2$ and $F=32\mu \mathrm{J}/{\mathrm{cm}}^2$, using a logarithmic vertical scale, is shown as an inset in (b). Exponential fits to the data (see text) are shown as thin gray lines. In the inset, only the fitting of the spectrum measured at $32\mu \mathrm{J}/{\mathrm{cm}}^2$ to a single-component exponential decay function for $t>100\mathrm{fs}$ is shown. To fit the data at $139\mu \mathrm{J}/{\mathrm{cm}}^2$ an additional component is needed.

Figure 4

Relaxation time (a) and excitation amplitude (b), obtained from the fitting to exponential decays (see text), as a function of the FS angle, $\varphi$. Lines are guides to the eye. The inset in (b) illustrates potential decay processes of photoexcited quasiparticles discussed in the text. The energy per pump pulse was kept constant, which lead in angle-dependent studies to a variation in $F$ due to changes in reflectivity and illuminated area. The data were corrected accordingly.