Transient terahertz photoconductivity of insulating cuprates

We establish a detailed phenomenology of photocarrier transport in the copper oxide plane by studying the transient terahertz photoconductivity of ${\mathrm{Sr}}_2{\mathrm{CuO}}_2{\mathrm{Cl}}_2$ and ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_6$. The peak photoconductivity saturates with fluence, decays on multiple picosecond timescales, and evolves into a state characterized by activated transport. The time dependence shows little change with fluence, indicating that the decay is governed by first-order recombination kinetics. We find that most photocarriers make a negligible contribution to the dc photoconductivity, and we estimate the intrinsic photocarrier mobility to be 0.6–0.7 ${\text{cm}}^2/\text{V}\text{s}$ at early times, comparable to the mobility in chemically doped materials.

Figure 1

Transient terahertz photoconductivity of ${\mathrm{Sr}}_2{\mathrm{CuO}}_2{\mathrm{Cl}}_2$. (a) Equilibrium optical conductivity from Zibold et al. [31], annotated to indicate the visible pump photon energy and the terahertz probe photon energy range. Inset: Schematic of the experimental geometry. The pump excites photocarriers in the sample, and the terahertz probe pulse measures the photoconductivity as a function of time. After passing through the sample, the terahertz waveform $E\left(t\right)$ is measured in the time domain by repetitive sampling of the electric field at the terahertz measurement time $t$; the red marker indicates the point associated with $t=2.3$ ps. We measure the change in $E\left(t\right)$ in response to a pump pulse that precedes the measured field point by a time delay $\tau$, to determine $\mathrm{\Delta }E(t,\tau )$. (b) Measurements at pump fluence $F=245\mu \text{J}/{\text{cm}}^2$ of $\mathrm{\Delta }E(t,\tau )$ relative to the background (obtained at $\tau =-14.7$ ps) for $\tau =$ 1.3, 4.0, 16.0, and 75.4 ps. Also shown is the reference field $E\left(t\right)$, which is transmitted through the sample without pump excitation. All curves are normalized to $E_p$, the peak value of $E\left(t\right)$, with different vertical scales for $\mathrm{\Delta }E(t,\tau )/E_p$ (left) and $E\left(t\right)/E_p$ (right), as indicated by the arrows.

Figure 2

Schematic of the photoexcitation process in the ${\mathrm{CuO}}_2$ plane, simplified by ignoring lattice distortions and quantum fluctuations of both spin and charge. Singly occupied Cu($3d_{x^2-y^2}$) orbitals are gray, and $\sigma$-bonded O($2p$) orbitals are red. Blue arrows indicate the spin orientation of holes that occupy each Cu($3d_{x^2-y^2}$) orbital in an antiferromagnetic arrangement at equilibrium. (a) The pump field transfers a hole from a Cu($3d_{x^2-y^2}$) orbital to a neighboring O($2p$) orbital. The pink circle denotes the negatively-charged spinless copper site, while the green circle indicates positive charge distributed among symmetry-equivalent oxygen orbitals. The copper and oxygen holes form a Zhang-Rice spin singlet [33], represented as spinless in the subsequent panel. (b) A probe electric field, applied in the direction of the black arrow in the upper right corner of each panel, causes the photoexcited charge carriers to move, which in turn disrupts the antiferromagnetic order. Dotted red lines indicate unfavorable magnetic bonds that each cost an energy $J/2$.

Figure 3

Room-temperature fractional change in the peak THz field amplitude transmitted through SCOC after photoexcitation with $F=245\mu \text{J}/{\text{cm}}^2$. Each point represents an average over $N>300$ individual measurements, and the error bars show the standard error, estimated with a bootstrap method. The solid line depicts a model of multiple exponential decays convolved with a Gaussian pulse shape, as described in the text. Markers identify $\tau =1.3$ ($\circ$), 4.0 ($\diamond$), 16.0 ($▿$), and 75.4 ($\square$) ps, as in Fig. 1. Inset: Room temperature photoconductivity spectra obtained from Fig. 1. Solid lines indicate mean values.

Figure 4

Peak photoconductivity as a function of incident fluence for (a) SCOC and (b) YBCO6. Solid lines show fits with the saturation model discussed in the text, with $F_0=221\mu \text{J}/{\text{cm}}^2$ for SCOC and $F_0=275\mu \text{J}/{\text{cm}}^2$ for YBCO6. The insets show the time-dependent photoconductivity, normalized to the peak value, for three different fluences: 69, 122, and 245 $\mu \text{J}/{\text{cm}}^2$ for SCOC and 66, 127, and 230 $\mu \text{J}/{\text{cm}}^2$ for YBCO6, denoted by blue, purple, and red curves, respectively. In YBCO6, the temporal response exhibits no significant fluence dependence, whereas in SCOC there is a weak increase in the overall decay rate with increasing fluence.

Figure 5

Time-dependent photoconductivity of SCOC with $F=240\mu \text{J}/{\text{cm}}^2$ (a) and YBCO6 with $F=220\mu \text{J}/{\text{cm}}^2$ (b), at $T=$ 15 K (blue), 150 K (purple), and 300 K (red); for clarity, the curves are shifted along the $\tau$ axis by 0, 3, and 6 ps, respectively. Insets: Photoconductivity at the peak (dark blue circles, left axis) and over the tail (gold squares, right axis) of the time-dependent photoconductivity curves shown in the main panels, as a function of base temperature $T$. Tail photoconductivity is the average over $100<\tau <150\text{ps}$. Dashed lines show fits of ${\sigma }_{1p}\left(T\right)=1/({\rho }_0+A{T}^2)$ to the peak data; dotted lines show fits of ${\sigma }_{1t}={\sigma }_{0}exp(-{\varepsilon }_A/k_B{T}_{\text{eff}})$ to the tail data, using a laser-heated effective temperature $T_{\text{eff}}={(T^4+T_{\ell }^4)}^{1/4}$ as described in the text.