Relaxation timescales and electron-phonon coupling in optically pumped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ revealed by time-resolved Raman scattering

Time-resolved measurements provide a new way to disentangle complex interactions in quantum materials due to their different timescales. We used pump-probe Raman scattering to investigate the apical oxygen vibration in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ under nonequilibrium conditions. Time dependence of the phonon population demonstrated strong electron-phonon coupling. Most importantly, the phonon shifts to a higher energy due to transient smearing of the Fermi surface in a remarkable agreement with diagrammatic theory. We also discuss insights into photoinduced superconductivity reported at lower doping that follow from these results.

Figure 1

Time-resolved Raman scattering (TRR) setup and key results. (a) Schematic of the TRR experiment and the color map showing representative data on the anti-Stokes (AS) side of the spectrum obtained with the sample at 300 K. Negative time corresponds to the probe pulse arriving before the pump pulse when the system is still at thermal equilibrium. Most intensity in the peak is from the apical oxygen phonon whose atomic displacements are indicated by green arrows in the schematic of the ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$ unit cell to the right of the color map. (b) Comparison of diagrammatic theory [38] and experiment for the dependence of phonon energy as a function of electronic temperature at delay times up to 600 fs. The temperature in the cryostat was 10 K/300 K in the top/bottom panels, respectively. Impurity scattering of 20 meV was added to the theory curve in the upper panel, but not to the lower panel, since scattering by phonons at 300 K is greater. Unrenormalized phonon energy was picked to obtain good agreement of theory with experiment at thermal equilibrium [38].

Figure 2

Raw data and phonon temperature at two doping levels. (a) Background-subtracted TRR spectra at different delay times with the cryostat at 300 K (black circles). The peaks at $\pm 500{\mathrm{cm}}^{-1}$ are Stokes ($+$) and anti-Stokes ($-$) phonon peaks. Red line is a guide to the eye representing smoothed data without the pump. Large peak widths are due to the increased energy width of the pulsed laser. (b) Phonon temperature as a function of time after photoexcitation at optimal doping and reduced doping where photoinduced superconductivity was reported earlier [9]. Temperature in the cryostat of 100 K and pump fluence of 8 mJ/${\mathrm{cm}}^2$ were the same as in Ref. [9]. Note that pump energy is absorbed first by electron-hole pairs, which then thermalize with the apical oxygen phonons; i.e., electronic temperature never drops below the phonon temperatures.

Figure 3

Phonon temperature and energy together with fits to the two-temperature model. Pump (probe) fluence was 1.4 mJ/${\mathrm{cm}}^2$ (15 $\mu \mathrm{J}$/${\mathrm{cm}}^2$). $T_{\mathrm{cryo}}$ was 250 K. Black line represents hot phonons; red, hot electrons; blue, cold phonons. The electronic temperature curves in (a) and (b) are the same. Inset to (a) illustrates the behavior at large delay times for the sample in air at 300 K. Dashed blue line in (b) is the measured pump-probe cross correlation centered at $t=0$.

Figure 4

Dependence on pump power, P, and $T_{\mathrm{cryo}}$. (a) Phonon hardening at 200 fs [$E_{ph}\left(200\text{fs}\right)-E_{ph}(-1000\text{fs})$] as a function of $T_{\mathrm{cryo}}$ at $P=27$ mW. Inset: Phonon hardening at $T_{\mathrm{cryo}}=10$ K as a function of P. (b) Phonon temperature at 200 fs and 1 ps as a function of $T_{\mathrm{cryo}}$ at $P=27$ mW (fluence of 1.4 mJ/${\mathrm{cm}}^2$). Note that $T_{el}=T_{ph}$ at 1 ps. Inset: $T_{ph}$ at 200 fs at $T_{\mathrm{cryo}}=10$ K as a function of P. (c) Electron-phonon coupling constant $\lambda$ together with the anharmonic scattering rate $1/\tau$. See Supplementary Notes 2 and 3 for details on how $\tau$ and $\lambda$ were calculated [41]