Quasiparticle dynamics in high-temperature superconductors far from equilibrium: An indication of pairing amplitude without phase coherence

We perform time-resolved photoelectron spectroscopy measurements of optimally doped $B{i}_{2}S{r}_{2}CaC{u}_2{O}_{8+\delta }$ (Bi-2212) and $B{i}_{2}S{r}_{2-x}L{a}_{x}Cu{O}_{6+\delta }$ (Bi-2201). The electron dynamics shows that inelastic scattering by nodal quasiparticles decreases when the temperature is lowered below the critical value of the superconducting phase transition. This drop in electronic dissipation is astonishingly robust and survives to photoexcitation densities much larger than the value sustained by long-range superconductivity. The unconventional behavior of quasiparticle scattering is ascribed to superconducting correlations extending on a length scale comparable to the inelastic path. Our measurements indicate that strongly driven superconductors enter in a regime without phase coherence but finite pairing amplitude. The latter vanishes near to the critical temperature and has no evident link to the pseudogap observed by angle-resolved photoelectron spectroscopy.

Figure 1

(a) Horizontal and (b) vertical profiles of the pump and probe beam on the camera. The best spatial overlap on the camera results in the highest pump-probe signal.

Figure 2

The data of this figure have been acquired on optimally doped Bi-2212 ($T_c=91$ K) at $T=150$ K. (a) Map of the photoelectron intensity integrated in a small energy interval centered around the Fermi level. The black line visualizes the cut along the nodal direction where we perform tr-ARPES measurements. (b) Photoelectron intensity map showing the quasiparticle dispersion along the nodal direction without the pump pulse. (c) Photoelectron intensity map acquired with a pump pulse at a delay time of 50 fs. (d) Pump-on minus pump-off intensity map at delay time $t=50$ fs. The dashed lines indicate the areas where the signals of the photoexcited electrons (blue) and photoexcited holes (red) have been integrated. (e) Energy distribution curves extracted at the Fermi wave vector and acquired with (blue) or without (red) a pump pulse. (f) Temporal evolution of the photoexcited electrons (blue) and holes (red) acquired with a fluence of $60\mu \mathrm{J}/{\mathrm{cm}}^2$. The solid line is a biexponential fit convoluted with our cross correlation.

Figure 3

The data of this figure have been acquired on optimally doped Bi-2212 ($T_c=91$ K) with a pumping fluence $60\mu \mathrm{J}/{\mathrm{cm}}^2$. (a) Dynamics of photoexcited quasiparticles acquired at different temperatures. The solid lines are biexponential fits $A_{1}exp(-t/{\tau }_1)+A_{2}exp(-t/{\tau }_2)$. The colored areas underneath stand for the slow component $A_{2}exp(-t/{\tau }_2)$. The curves have been shifted by an arbitrary offset for better clarity. (b) Relative weight of the fast component $A_1$ as a function of temperature. (c) Fast decay time ${\tau }_1$ as a function of temperature. The blue and red marks in (b) and (c) are two different cleaves while the dashed line is a guide to the eye.

Figure 4

Dynamics of photoexcited quasiparticles in Bi-2201 ($T_c=28$ K) (circles) and Bi-2212 ($T_c=91$ K) (triangles) acquired with a pump fluence of $60 \mu \mathrm{J}/{\mathrm{cm}}^2$ at a base temperature $T=35$ K. The solid lines are biexponential fits. The fast component $A_1$ is small only in the superconducting sample Bi-2212.

Figure 5

The data of this figure have been acquired on optimally doped Bi-2212 ($T_c=91$ K) at $T=35$ K. (a) Dynamics of photoexcited quasiparticles acquired at different pumping fluences. The solid lines are biexponential fits while the colored areas underneath stand for the slow component. The curves have been shifted by an arbitrary offset for better clarity. (b) Maximal value of the photoinduced signal $I_m$ as a function of pump fluence. The dashed line is a guide to the eye. (c) Relative weight of the fast component $A_1$ as a function of pump fluence. The dashed line is a guide to the eye and the solid area is the fluence range where phase stiffness is not totally destroyed by the optical pump pulse.

Figure 6

(a) Dynamics of photoexcited quasiparticles acquired on optimally doped Bi-2212 ($T_c=91$ K) at $T=35$ K and a pumping fluence of $280 \mu \mathrm{J}/{\mathrm{cm}}^2$. (b) Momentum distribution curves extracted by integrating the intensity maps in an energy window of 30 meV below the Fermi level. The red and blue curves stand for data acquired without a pump pulse (red) and 50 fs after the arrival of a pump pulse with $120 \mu \mathrm{J}/{\mathrm{cm}}^2$ (blue).