Impact ionization processes in a photodriven Mott insulator: Influence of phononic dissipation

We study a model for photovoltaic energy collection consisting of a Mott-insulating layer in presence of acoustic phonons, coupled to two wide-band fermion leads at different chemical potentials and driven into a nonequilibrium steady state by a periodic electric field. We treat electron correlations with nonequilibrium dynamical mean-field theory using the so-called auxiliary master-equation approach as impurity solver and include dissipation by acoustic phonons via the Migdal approximation. For a small hybridization to the leads, we obtain a peak in the photocurrent as a function of the driving frequency which can be associated with impact ionization processes. For larger hybridizations the shallow peak suggests a suppression of impact ionization with respect to direct photovoltaic excitations. Acoustic phonons slightly enhance the photocurrent for small driving frequencies and suppress it at frequencies around the main peak at all considered hybridization strengths.

Figure 1

Schematic representation of the setup. A central, correlated layer with local Hubbard interaction $U$ and e-ph coupling $g$ (green) is sandwiched between two noninteracting layers (red) via the hybridization $v$ (black). The latter are in turn coupled to wide-band fermion reservoirs (blue) with different chemical potentials ${\mu }_{\text{l}/\text{r}}$, which introduce broadenings ${\mathrm{\Gamma }}_{\text{l}/\text{r}}$.

Figure 2

Schematic representation of the processes occurring in the model considered. Red bands on the left and right describe the leads' DOS, where the dark color highlights occupied states and the light color empty states. Green bands are the LHB and UHB of the central layer. The vertical axis represents the energy. Due to the hybridization with the metallic leads only a pseudogap ${\mathrm{\Delta }}_{\text{pg}}$ is present between the Hubbard bands. (a) Sketches the quantities introduced at the beginning of Sec. 4. (b) Illustrates a direct excitation process, in which an electron is excited by a photon with energy $\mathrm{\Omega }$ (yellow arrow) to the UHB and escapes into the right lead (red arrow). (c) Displays an II process, where the photoexcited electron in the UHB excites a second electron from LHB to UHB (black arrows) and both escape into the right lead. In the nonequilibrium steady state considered here, only processes recovering the initial configuration are allowed.

Figure 3

(a) Time-averaged steady-state current $j$ and (b) double occupancy $N_{\text{D}}$ plotted as a function of the driving frequency $\mathrm{\Omega }$. Results are shown for different values of the lead-layer hybridization $v$ as well as without and with e-ph interaction. Default parameters are specified at the beginning of Sec. 4.

Figure 4

Spectral function $A\left(\omega \right)$ (solid line) and occupation function $N\left(\omega \right)$ (shaded area) at (a) $\mathrm{\Omega }=5$ and (b) $\mathrm{\Omega }=11$ for $v=0.4$ and 0.8 for the EO system. Default parameters are specified at the beginning of Sec. 4.

Figure 5

(a) Time-averaged steady-state current $j$ and (b) double occupancy $N_{\text{D}}$ as a function of $\mathrm{\Omega }$, at $v=0.8$ for $E_0=3,4$ for the EO system. Default parameters are specified at the beginning of Sec. 4.

Figure 6

Spectral function $A\left(\omega \right)$ (solid line) and occupation function $N\left(\omega \right)$ (shaded area) at $\mathrm{\Omega }=11$ without and with e-ph interaction, for (a) $v=0.4$ and (b) $v=0.8$. Default parameters are specified at the beginning of Sec. 4.

Figure 7

(a) Time-averaged steady-state current $j$ and (b) double occupancy $N_{\text{D}}$ as a function of $\mathrm{\Omega }$, for $v=0.4,0.8$, at phonon cutoff frequencies ${\omega }_{\text{ph}}=0.025,0.05$. Default parameters are specified at the beginning of Sec. 4.

Figure 8

(a) Time-averaged steady-state current $j$ and (b) double occupancy $N_{\text{D}}$ as a function of $\mathrm{\Omega }$, for $v=0.5,0.6,0.7$, without and with e-ph interaction. Default parameters are specified at the beginning of Sec. 4.