Charge recombination in undoped cuprates

We theoretically analyze the process of charge recombination in the planar Mott-Hubbard insulators with the aim to explain the short picosecond-range lifetimes of photoexcited carriers, experimentally studied via pump-probe experiments on the undoped cuprates. The recombination mechanism consists of two essential ingredients: the formation of a metastable $s$-type bound holon-doublon pair, i.e., the Mott exciton, and the decay of such an excitonic state via the multimagnon emission. In spite of the large gap that requires many bosons to be emitted, the latter process is fast due to a large exchange scale and strong charge-spin coupling in planar systems. As the starting microscopic model we consider the single-band Hubbard model and then a more realistic three-band model for cuprates, both leading to the same minimal one. The decay rate of the exciton is evaluated numerically via the Fermi golden rule, having consistency also with the direct time-evolution calculation. The decay rate reveals exponential dependence on the ratio of the Mott-Hubbard gap and the exchange coupling, the result qualitatively reproduced also within a toy exciton-boson model.

Figure 1

Comparison of coupling parameters $r^i=2r^d,r^{hd},2r^h$ for different recombination channels with the (rescaled) exchange coupling $J/2$ as a function of charge-transfer energy ${\Delta }_0$. For other parameters, standard values are used.

Figure 2

Charge density correlation $D_j$.

Figure 3

Exciton recombination rate $\Gamma$ vs $\Delta /J$ for different $J=0.3,0.4,0.6$ as calculated for $N=26$ sites.

Figure 4

Doublon (and also HD pair) occupation number $n_d$ (in logarithmic scale) as a function of time $\tau$, calculated for different gaps $\Delta =4.8,5.2,6.0$ and parameters $J=0.4$ for a system of size $N=26$.

Figure 5

Comparison of the exciton recombination rate $\Gamma$ vs gap $\Delta$ as calculated using the FGR (lines) and time evolution (dots) for $J=0.4$ and systems of size $N=20,26$.

Figure 6

Comparison of the result for $\tilde{\Gamma }=\Gamma /g_{rc}^2$, if calculated with (a) the numerical evaluation of $\Gamma$ from Eq. (39), (b) the saddle-point result for a numerically (exactly) established saddle, (c) the saddle-point result for an approximate saddle [Eq. (42)], and (d) a compact form of Eq. (44). Parameters ${\omega }_0=5,\xi =3,\sigma ={\omega }_0/4$ are used so that numerical integration (a) is well defined.

Figure 7

Fit of Eq. (44) with $\xi ,g_{rc}$ as the fitting parameters to the numerical result (num) for $\Gamma \left(\Delta \right)$ obtained on 2D system (as described in previous section) for $J=0.3,0.4,0.5$.

Figure 8

Values of the fitting parameters $\xi$ (boson coupling) and $g_{rc}$ (recombination prefactor) as a function of $J$. For comparison, $|{\epsilon }_b|/J,t/J$ are plotted as well. Prefactor $1/3$ was used with $\xi$ and $t/J$ to unify the scales.

Figure 9

The error in recombination coupling parameters, $\delta r=r_{\mathrm{num}}-r_{\mathrm{appr}}$, originating in an approximate calculation [Eq. (A6)] of the holon state $|H\rangle$ and its energy $E_H$ as a function of ${\Delta }_0$. For other parameters standard values are used.