Photoexcited states in correlated band insulators

We study the photoexcitation dynamics of correlated band insulators, using nonequilibrium dynamical mean-field theory for the ionic Hubbard model. We find two distinct behaviors, depending on the ratio of the on-site interaction $U$ and the bare band gap $\mathrm{\Delta }$. For small interactions, the relaxation is characterized by intraband carrier scattering in relatively rigid bands, leading to a nonthermal intermediate state with separate thermal distributions of electrons and holes. This behavior can be viewed as typical for a band insulator with weak interactions. For larger interaction, on the other hand, we observe a strong modification of the electronic spectrum and a filling-in of the gap after photoexcitation, along with a rapid thermalization of the system. The two behaviors therefore provide a dynamical distinction of a correlated band insulator and a band insulator, which can differ even when the spectra of the two systems are similar in equilibrium. The crossover happens when the interaction $U$ is comparable to $\mathrm{\Delta }$.

Figure 1

(a) Double occupancy of the photoexcited system for different values of $U$. The excitation density is chosen such that $T_{\mathrm{eff}}=1$. Solid curves show the numerical data, and red dashed lines show exponential fits. Small arrows indicate the double occupancy in thermal equilibrium. Zero time ($t=0$) is the starting time of simulations. (b) Difference of the double occupancy in equilibrium at temperature $T=T_{\mathrm{eff}}$ and in the photoexcited system. (c) Relaxation time of the double occupancy for different values of $U$. The dashed curve is a fit to the relaxation times with the relation $\frac{a}{U^2}$.

Figure 2

Top: Difference of the double occupancy in thermal equilibrium at temperature $T=T_{\mathrm{eff}}$ and in the time-evolved state for different values of the ionic potential: (a) $\mathrm{\Delta }=0.2$, (b) $\mathrm{\Delta }=0.4$, (c) $\mathrm{\Delta }=0.6$, and (d) $\mathrm{\Delta }=0.8$. The excitation density is chosen such that $T_{\mathrm{eff}}=0.3$ (black circles) or $T_{\mathrm{eff}}=1.0$ (red squares). Bottom: Relaxation times of the double occupancy.

Figure 3

Top: Difference of the sublattice occupancy in thermal equilibrium ($m_{\mathrm{th}}$) at temperature $T=T_{\mathrm{eff}}$ and in the time-evolved state ($m_{t=\infty }$) for different values of the ionic potential: (a) $\mathrm{\Delta }=0.2$, (b) $\mathrm{\Delta }=0.4$, (c) $\mathrm{\Delta }=0.6$, and (d) $\mathrm{\Delta }=0.8$. The excitation density is chosen such that $T_{\mathrm{eff}}=0.3$ (black circles) or $T_{\mathrm{eff}}=1.0$ (red squares). Bottom: Relaxation times of the sublattice occupancy.

Figure 4

(a) Left: Spectral function $A^R(t=180,\omega )$ for different values of $U$ and $\mathrm{\Delta }=0.4$. Right: The corresponding occupied density of states $A^{<}(t=180,\omega )$ above the Fermi level. The green and pink curves correspond to the spectral functions of the excited system (Exc) and the system in thermal equilibrium (Thermal), respectively. The black dashed lines indicate the Hartree-Fock spectral function (see text). (b) Same as (a), but for $\mathrm{\Delta }=0.6$. The excitation density is chosen such that $T_{\mathrm{eff}}=1$.

Figure 5

Electronic distribution functions $F_A(t=180,\omega )$ [Eq. (11)] for different values of $U$ and ionic potential $\mathrm{\Delta }=0.4$ (top panel) and $\mathrm{\Delta }=0.6$ (bottom panel).

Figure 6

Relaxation times of the double occupancy for different values of $\mathrm{\Delta }$ and $U>\mathrm{\Delta }$. The dashed curves indicate power-law fits.

Figure 7

The value of the retarded spectral function at $\omega =0$ for large time $t=180$ in the photoexcited state (excitation density such that $T_{\mathrm{eff}}=1$).

Figure 8

Occupied density of states above the Fermi level at different times for $\mathrm{\Delta }=0.4$ and $T_{\mathrm{eff}}=1.0$. Insets: Integrated weight of the occupied density of states, $W\left(t\right)={\int }_0^{\infty }{A}^{<}(t,\omega )d\omega$, above the Fermi level.

Figure 9

Time-dependent change in the occupied density of states for excitation density corresponding to $T_{\mathrm{eff}}=1.0$, $\mathrm{\Delta }=0.4$, and (a) $U/\mathrm{\Delta }=1.0$ or (b) $U/\mathrm{\Delta }=1.375$. The up (down) arrows indicate frequencies at which a rapid increase (decrease) is observed more strongly during the relaxation.