Many-body recombination in photoexcited insulating cuprates

We study the pump-probe response of three insulating cuprates and develop a model for its recombination kinetics. The dependence on time, fluence, and both pump and probe photon energies implies many-body recombination on femtosecond timescales, characterized by anomalously large trapping and Auger coefficients. The fluence dependence follows a universal form that includes a characteristic volume scale, which we associate with the holon-doublon excitation efficiency. This volume varies strongly with pump photon energy and peaks at nearly twice the charge-transfer energy, suggesting that the variation is caused by carrier multiplication through impact ionization.

Figure 1

Linear and nonlinear optical response of insulating cuprates at room temperature. (a) Optical conductivity for YBCO6 [31], SCOC [32], and LCO [33]. Markers indicate the probe energy $E_0$ with the peak pump-probe response for each material (1.72, 1.90, and 2.07 eV for YBCO6, SCOC, and LCO, respectively), and the arrow indicates the pump photon energy $E_{\text{p}}=2.88\mathrm{eV}$ used for panels (b) and (c). (b) Pump-probe response spectra, $\mathrm{\Delta }R(0,E;E_{\text{p}},F)/R\left(E\right)$, with $E_{\text{p}}=2.88\mathrm{eV}$ and $F=(0.83\pm 0.05)\text{mJ}/{\text{cm}}^2$, normalized to $|\mathrm{\Delta }R(0,E_0;E_{\text{p}},F)/R\left(E_0\right)|$ (0.096, 0.19, and 0.052 for YBCO6, SCOC, and LCO, respectively) and plotted as a function of $\delta E=E-E_0$ for each material. (c) Time dependence of the peak response, $\mathrm{\Delta }R(t,E_0;E_{\text{p}},F)/R\left(E_0\right)$, for the pump conditions in (b), normalized to $\mathrm{\Delta }R(0,E_0;E_{\text{p}},F)/R\left(E_0\right)$. (d), (e) Schematic of a recombination process in an antiferromagnetic insulator [9, 10]. Blue arrows represent electrons and their spin direction. When an unoccupied site recombines with a doubly occupied site (d), it dissipates the Mott gap energy into the spin system (e).

Figure 2

Fluence dependence of (a) the peak amplitude $\mathrm{\Delta }R(0,E_0,E_{\text{p}})/R\left(E_0\right)$ and (b) the decay rate $\gamma =-\left[d\left(\mathrm{\Delta }R\right)/dt\right]/\mathrm{\Delta }R$ evaluated at $t\approx 0.2$ ps for YBCO6 and SCOC with $E_{\text{p}}=2.88\mathrm{eV}$ and single-crystal LCO with $E_{\text{p}}=2.69\mathrm{eV}$, all at room temperature. Lines in (a) represent least-squares fits to Eq. (1) with $F_{\text{s}}=(0.96\pm 0.08),(0.49\pm 0.05),$ and $(0.6\pm 0.2){\mathrm{mJ}/\mathrm{cm}}^2$ and $\alpha =0.18\pm 0.01,0.25\pm 0.02,$ and $0.05\pm 0.01$ for YBCO6, SCOC, and LCO, respectively. Lines in (b) show $\gamma \left(F\right)={\gamma }_0{(1+F/F_{\text{s}})}^{-1}$, the decay rate expected if the saturation shown in (a) were entirely due to nonlinearity in $n_{\text{ex}}\to \mathrm{\Delta }R$, with fluence-independent kinetics. For each material, ${\gamma }_0$ is chosen to make the curve pass through the measurement at the highest fluence. (c) The differential reflectance of thin-film LCO saturates with fluence, even as (d) the transmitted pump fluence ($\square$) and reflected pump fluence ($\diamond$) both remain linear with incident fluence. (e) Fluence reflected from single-crystal samples of YBCO6, SCOC, and LCO at $E_{\text{p}}=3.10\text{eV}$ as a function of incident pump fluence, with lines showing linear fits.

Figure 3

Scaling plot of the peak differential reflectance of YBCO6 at $E=1.70\mathrm{eV}$ for various pump photon energies at room temperature. Differential reflectance measurements were fit with Eq. (1) to obtain estimates of $\alpha$ and $F_{\text{s}}$ for each value of $E_{\text{p}}$, then normalized by $\alpha$ and plotted as a function of normalized fluence $F/F_{\text{s}}$. The black curve shows Eq. (1) using the same procedure. The inset shows the differential reflectance with $E_{\text{p}}=2.46\mathrm{eV}$ at $E=1.70\mathrm{eV}$ as a function of time (normalized to the peak value) for $F=0.4F_{\text{s}}$ (blue) and $F=2.8F_{\text{s}}$ (red), where $F_{\text{s}}=0.38 \mathrm{mJ}/{\mathrm{cm}}^2$; the black dotted curve shows the normalized response expected for $F=2.8F_{\text{s}}$, given $\mathrm{\Delta }R\left(t\right)/R$ at $F=0.4F_{\text{s}}$ and assuming $\mathit{\rho }$ independent of $n_{\text{ex}}$.

Figure 4

Joint variation of $\mathrm{\Delta }R/R$ with fluence and time in LCO with $E_{\text{p}}=3.10\text{eV}$ and $E=E_0=2.07\text{eV}$. (a) Time dependence for equally spaced values of fluence, with $F_0=450{\mathrm{mJ}/\mathrm{cm}}^2$. (b) Fluence dependence of $\mathrm{\Delta }R/R$, averaged over the three temporal ranges shown as colored bands in (a) and normalized so that the response at each fluence has unit slope in the limit $F\to 0$. Curves show fits to Eq. (1) and arrows indicate the fluences shown in (a).

Figure 5

(a) Differential reflectance at room temperature of YBCO6 at $E=1.70\mathrm{eV}$ with $E_{\text{p}}=2.46\mathrm{eV}$ as $F$ increases from $0.04\mathrm{mJ}/{\mathrm{cm}}^2$ (blue) to $1.07\mathrm{mJ}/{\mathrm{cm}}^2$ (red). (b) Model results with $\eta =1, {\gamma }_{\text{h}}=1.3{\text{ps}}^{-1}, {\gamma }_{\text{d}}=32{\text{ps}}^{-1}, C_{\text{h}}=7.8\times {10}^{-26}{\text{cm}}^6/\text{s}$, and $\chi =280e^{-2.75i}\text{Cu}$. Markers in (a) and (b) indicate the half-maximum point on the leading edge, which shows a temporal shift $\mathrm{\Delta }{t}_{1/2}$ to earlier times. (c) Fluence dependence of $\mathrm{\Delta }{t}_{1/2}$ for the points shown in (a), fit with $\mathrm{\Delta }{t}_{1/2}={\alpha }_{1/2}(F/F_{1/2}){(1+F/F_{1/2})}^{-1}$ (black line).

Figure 6

Saturation parameters at room temperature as a function of excitation energy $\delta E_{\text{p}}=E_{\text{p}}-E_0$. (a) Effective excitation volume $v$. (b) Saturated differential reflectance amplitude $\alpha$, normalized for each material to its average $\langle \alpha \rangle$ over all measured $E_{\text{p}}$.