Photoinduced collective mode, inhomogeneity, and melting in a charge-order system

We theoretically investigate photoresponses of a correlated electron system upon stimuli of a pulsed laser light. Real-time dynamics of an interacting spinless fermion model on a one-dimensional chain, as a model of charge order (CO), are numerically simulated using the time-dependent Hartree-Fock method. In particular, we discuss the differences between two situations as the initial state: the homogeneous order and the presence of a domain wall, i.e., a kink structure embedded in the CO bulk. Coherent dynamics are seen in the former case: When the frequency of the pump light ${\omega }_p$ is varied, along with single particle excitations across the CO gap (${\mathrm{\Delta }}_{\mathrm{CO}}$), the resonantly-excited collective phase mode near ${\omega }_p\simeq {\mathrm{\Delta }}_{\mathrm{CO}}/2$ efficiently destabilizes CO. In clear contrast, in the latter case, when ${\omega }_p$ is tuned at such in-gap frequencies and the intensity of light is sufficiently large, inhomogeneity spreads out from the kink to the bulk region through kink creations. Moreover, even stronger intensity induces the inhomogeneous melting of CO where the CO gap is destroyed.

Figure 1

(a) $\tau$ dependence of order parameter $\delta \left(\tau \right)$ for an even number of sites, with two pump-light frequencies: ${\omega }_p={\mathrm{\Delta }}_{\mathrm{CO}}=6.45$ and ${\omega }_p={\mathrm{\Delta }}_{\mathrm{CO}}/2$, for different intensity $A_p$. (b) A closer look at the latter case for $A_p=1$ together with real and imaginary parts of the bond orders ${\chi }_i\left(\tau \right)$ for even and odd $i$. The light and dark shaded areas show the time domain where the pump light is applied and one period of oscillation, respectively.

Figure 2

Two-dimensional plots on the {${\omega }_p,A_p$} plane of the time averaged photoresponses for the $N=500$ sites case: (a) decrease in the order parameter $\mathrm{\Delta }\delta$ renormalized by ${\delta }_0$, (b) standard deviation $\sigma$ in $\delta \left(\tau \right)$, (c) effective absorbed photon number $N_{ph}$, and (d) in-gap density of states (dos). Their definitions are depicted in the text.

Figure 3

Time evolution of $\langle n_i\rangle$ on each site, plotted for $i=$ 76 to 426, among $N=$ 501 sites. (a) The initial state having a kink structure centered at $i=250–251$. (b) $A_p=$ 4 and (c) $A_p=$ 8, for time $\tau =$ 20 and 40 $[{\omega }_p={\mathrm{\Delta }}_{\mathrm{CO}}/2]$. On the right of each plot, the temporary density of states (dos) is plotted, where the Fermi energy is set to the origin.

Figure 4

$\tau$ dependence of the averaged “order parameter” ${\delta }_{\mathrm{av}}\left(\tau \right)$ for $N=501$. The frequency of the pump light is ${\omega }_p={\mathrm{\Delta }}_{\mathrm{CO}}/2$, for different intensity $A_p$. The shaded area shows the time domain where the pump light is applied.

Figure 5

Two-dimensional plots on the {${\omega }_p,A_p$} plane of the time averaged photoresponses for the $N=501$ sites case: (a) decrease in the order parameter $\mathrm{\Delta }\delta$ renormalized by ${\delta }_0$, (b) standard deviation $\sigma$ in $\delta \left(\tau \right)$, (c) effective absorbed photon number $N_{ph}$, and (d) in-gap density of states (dos). Their definitions are depicted in the text.

Figure 6

The linear optical absorption spectrum $\alpha \left(\omega \right)$ using the time-dependent Hartree-Fock method, for $V=4$.

Figure 7

$\tau$ dependence of order parameter $\delta \left(\tau \right)$ and the real and imaginary parts of the bond orders ${\chi }_i\left(\tau \right)$ for even and odd $i$ for $N=500$. (a) ${\omega }_p={\mathrm{\Delta }}_{\mathrm{CO}}/2=3.225,A_p=1$ as in the main text [Fig. 1] and (b) ${\omega }_p=2.15,A_p=1$. The light and dark shaded areas show the time domain where the pump light is applied and one period of the excited oscillation, respectively.

Figure 8

Examples of temporary density of states for the $N=500$ case, corresponding to the case in Fig. 1 (a), ${\omega }_p={\mathrm{\Delta }}_{\mathrm{CO}}/2$. The data are for $\tau =10,20,$ and 30.

Figure 9

Two-dimensional plots on the {${\omega }_p,A_p$} plane of the photoresponses for $V=2$, with (a) $N=500$ and (b) $N=501$ sites. The plotted quantities are: (i) decrease in the order parameter $\mathrm{\Delta }\delta$ renormalized by ${\delta }_0$, (ii) standard deviation $\sigma$ in $\delta$, (iii) effective absorbed photon number $N_{ph}$, and (iv) in-gap density of states (dos). Their definitions are depicted in the main text.