Dynamics of photodoped charge transfer insulators

We study the dynamics of charge transfer insulators after photoexcitation using the three-band Emery model and a nonequilibrium extension of $\mathrm{Hartree}-\mathrm{Fock}+\mathrm{EDMFT}$ (extended dynamical mean field theory) and $\mathit{GW}+\mathrm{EDMFT}$. While the equilibrium properties are accurately reproduced by the Hartree-Fock treatment of the ligand bands, dynamical correlations are essential for a proper description of the photodoped state. Photodoping leads to a renormalization of the charge transfer gap and to a substantial broadening of the bands. We calculate the time-resolved photoemission spectrum and optical conductivity and find qualitative agreement with experiments. Our formalism enables the realistic description of nonequilibrium phenomena in materials with ligand bands. It provides a tool to explore the optical manipulation of interaction and correlation effects, including insulator-metal and magnetic transitions.

Figure 1

Orbitally resolved spectral function obtained in the $GW+\mathrm{EDMFT}$ (black) and $\mathrm{HF}+\mathrm{EDMFT}$ (red) approximation for the CT (a) and LCO (b) setups. The full (dashed) lines represent the $d$ ($p_x$ and $p_y$) orbitals.

Figure 2

Dynamics after photoexcitation for the CT (top panels) and LCO (bottom panels) setups. The left panels show the change in the occupancy of the $d$ orbitals. The change in the $p$ orbital occupation is given by $\mathrm{\Delta }{n}_p=-\frac{1}{2}\mathrm{\Delta }{n}_d.$ The right panel shows the change in the density of $d$ holes $\mathrm{\Delta }{h}_d$ in the lower Hubbard band. The hole density on the $p$ orbital can be estimated as $\mathrm{\Delta }{h}_p=\frac{1}{2}\mathrm{\Delta }{n}_d$ and is shown by the dashed lines in the time interval [8:13] for clarity.

Figure 3

Time evolution of the spectral function $A_{\alpha }(\omega ,t)$ within $\mathrm{HF}+\mathrm{EDMFT}$ [(a) and (b)] and $GW+\mathrm{EDMFT}$ [(c) and (d)] for the CT (left panels) and LCO (right panels) setups, both excited with the pulse frequency $\mathrm{\Omega }=6.0\mathrm{eV}$. The black lines show the equilibrium spectra. Thick shaded (thin) lines represent the $d$ ($p_x$ and $p_y$) orbitals. The black vertical line and the arrow mark the peak position of the upper Hubbard band in equilibrium, the red ones indicate the Hartree shift, and the green ones correspond to the combined effect of Hartree shift and static reduction of the effective impurity interaction $\mathcal{U}(\omega =0).$

Figure 4

Time evolution of the screened interaction $W_d(t,\omega )$ for the CT (a) and LCO (b) setups, both excited with frequency $\mathrm{\Omega }=6.0\mathrm{eV}$. The black shaded line represents the equilibrium spectrum.

Figure 5

Time-dependent optical conductivity in the (11) direction $\sigma (\omega ,t_p)$ for the CT (a) and LCO (c) setups. The black lines represent the equilibrium data. (b) The difference from the equilibrium result $\mathrm{\Delta }\sigma (t_p,\omega )=\sigma (t_p,\omega )-{\sigma }^{\text{eq}}\left(\omega \right)$ for the delayed probe pulse at $t_p=7$ fs in both setups. (d) The gap size renormalization in the optical conductivity (Dyn) as a function of the photoexcited doublons and comparison with the static shift (Stat) ${\mathrm{\Sigma }}_H+\mathcal{U}(\omega =0)$.