Instantaneous charge and dielectric response to terahertz pulse excitation in TTF-CA

We present the results of exact numerical calculations of the dielectric properties of tetrathiafulvalene-$p$-chloranil (TTF-CA) using the extended Hubbard model. The electronic polarization ${\overline{P}}_{\mathrm{el}}$ of the ionic ground state is obtained by directly calculating the adiabatic flow of current. The direction of ${\overline{P}}_{\mathrm{el}}$ is opposite to polarization ${\overline{P}}_{\mathrm{ion}}$ owing to ionic displacement, and $|{\overline{P}}_{\mathrm{el}}|$ is much larger than $|{\overline{P}}_{\mathrm{ion}}|$, showing that, in the ionic phase, TTF-CA is an electric ferroelectric. Furthermore, we numerically calculate the dynamics induced by THz pulse excitation. In the ionic phase, there exists an almost exact linear relationship between $\mathrm{\Delta }\rho \left(t\right)$ and $E\left(t\right)$, and between $\mathrm{\Delta }{P}_{\mathrm{el}}\left(t\right)$ and $E\left(t\right)$ in the realistic range of the excitation magnitude, where $\mathrm{\Delta }\rho \left(t\right)\left[\mathrm{\Delta }{P}_{\mathrm{el}}\left(t\right)\right]$ is the charge transfer (electric polarization) variation induced by the THz pulse and $E\left(t\right)$ is the electric field of the pulse at time $t$. The absolute value of $\mathrm{\Delta }\rho \left(t\right)$ in the neutral phase is much smaller than that in the ionic phase. These results are consistent with those of experiments and originate from the adiabatic nature of the THz pulse excited state.

Figure 1

Schematic representation of the electronic structures of the (a) neutral and (b) ionic phases of TTF-CA. The horizontal lines show the highest occupied molecular orbital of D and the lowest unoccupied molecular orbital of A, and the arrows represent the electron spins. Neutral (ionic) D and A are denoted by ${\mathrm{D}}^0$ and ${\mathrm{A}}^0$ (${\mathrm{D}}^{+}$ and ${\mathrm{A}}^{-}$), respectively.

Figure 2

The ${\alpha }^{\prime }$ dependence of $\overline{\rho }$ for ${\beta }^{\prime }=0$ and ${\beta }^{\prime }=0.02$.

Figure 3

(a) $\mathrm{\Delta }\rho \left(t\right)$ and (b) $\mathrm{\Delta }{P}_{\mathrm{el}}\left(t\right)$ for $\overline{A}=-4$, $-3$, $-2$, $-1$, 1, 2, 3, 4, and 5 in the ionic phase (for ${\alpha }^{\prime }=0.13$ and ${\beta }^{\prime }=0.02$), shown with thick lines. The fitting curves $\mathrm{\Delta }\tilde{\rho }\left[E\left(t\right)\right]$ and $\mathrm{\Delta }{\tilde{P}}_{\mathrm{el}}\left[E\left(t\right)\right]$ are shown with thin lines.

Figure 4

$\mathrm{\Delta }\tilde{\rho }\left(E\right)$ and $\mathrm{\Delta }{\tilde{P}}_{\mathrm{el}}\left(E\right)$ for ${\alpha }^{\prime }=0.13$. The experimentally estimated values for $E=-38$ kV/cm are also shown.

Figure 5

(a) $\mathrm{\Delta }\rho \left(t\right)$ and (b) $\mathrm{\Delta }{P}_{\mathrm{el}}\left(t\right)$ for $\overline{A}=1$, 2, 3, and 4 in the neutral phase (for ${\alpha }^{\prime }=0.158$ and ${\beta }^{\prime }=0$).

Figure 6

The ${\beta }^{\prime }$ dependence of $\mathrm{\Delta }\rho \left(0\right)$ for $\overline{A}=0.1$ in the ionic (${\alpha }^{\prime }=0.13$) and neutral (${\alpha }^{\prime }=0.158$) states of TTF-CA.

Figure 7

(a) $\mathrm{\Delta }\rho \left(t\right)$ and (b) $\mathrm{\Delta }{P}_{\mathrm{el}}\left(t\right)$ for $\overline{A}=-1$, $-0.8$, $-0.6$, $-0.4$, $-0.2$, 0.2, 0.4, 0.8, and 1 in the ionic phase in the phase boundary region (for ${\alpha }^{\prime }=0.1445$ and ${\beta }^{\prime }=0.02$), shown by the thick lines. The fitting curves $\mathrm{\Delta }\tilde{\rho }(\left[\left(t\right)\right]$ and $\mathrm{\Delta }{\tilde{P}}_{\mathrm{el}}\left[E\left(t\right)\right]$ are represented by the thin lines.