Terahertz pulse induced transitions between ionic and neutral phases and electronic polarization reversal in TTF-CA

We have investigated the terahertz (THz)-pulse-induced dynamics of tetrathiafulvalene-$p$-chloranil near the boundary between the ionic and neutral phases with the use of exact numerical calculations of an extended Hubbard model coupled with lattice motion. For the ionic phase, when the applied electric field of the THz pulse opposes the electronic contribution to the electric polarization (electronic polarization) ${\overline{P}}_{\mathrm{el}}$ of the ground state and the maximum amplitude of electric field is greater than a threshold value, the THz-pulse excited state changes as ${\mathrm{I}}_{\mathrm{A}}\to \mathrm{N}\to {\mathrm{I}}_{\mathrm{B}}\to \mathrm{N}\to {\mathrm{I}}_{\mathrm{A}}\to \mathrm{N}\to \cdots ({\mathrm{I}}_{\mathrm{A}}$ ground-state case) or ${\mathrm{I}}_{\mathrm{B}}\to \mathrm{N}\to {\mathrm{I}}_{\mathrm{A}}\to \mathrm{N}\to {\mathrm{I}}_{\mathrm{B}}\to \mathrm{N}\to \cdots ({\mathrm{I}}_{\mathrm{B}}$ ground-state case), where N shows the neutral state, ${\mathrm{I}}_{\mathrm{A}}\left({\mathrm{I}}_{\mathrm{B}}\right)$ shows the ionic state with ${\overline{P}}_{\mathrm{el}}<0\left({\overline{P}}_{\mathrm{el}}>0\right)$, and the phase of the bond-length alternation of ${\mathrm{I}}_{\mathrm{A}}$ is opposite to that of ${\mathrm{I}}_{\mathrm{B}}$. For the neutral phase, when the maximum amplitude of the electric field is greater than a threshold value, the THz-pulse excited state changes as $\mathrm{N}\to {\mathrm{I}}_{\mathrm{B}}\to \mathrm{N}\to {\mathrm{I}}_{\mathrm{A}}\to \mathrm{N}\to {\mathrm{I}}_{\mathrm{B}}\to \cdots$ (positive electric field case) or $\mathrm{N}\to {\mathrm{I}}_{\mathrm{A}}\to \mathrm{N}\to {\mathrm{I}}_{\mathrm{B}}\to \mathrm{N}\to {\mathrm{I}}_{\mathrm{A}}\to \cdots$ (negative electric-field case). The phase transitions and electronic polarization reversal are driven by time variation of the lattice order parameter, which indicates the magnitude and phase of the bond-length alternation, and the lattice motion is induced by THz-pulse excitation through the electron–lattice coupling. Transitions between the ionic and neutral phases occur and electronic polarization reverses on a picosecond timescale together with the realizable magnitude of the THz pulse both in the ionic and neutral phases near the phase boundary.

Figure 1

Schematic representation of the electronic structures of (a) neutral phase $\left(\mathrm{N}\right)$, (b) ionic phases with A phase bond-length alternation $\left({\mathrm{I}}_{\mathrm{A}}\right)$, and (c) ionic phases with B phase bond-length alternation $\left({\mathrm{I}}_{\mathrm{B}}\right)$ of TTF-CA. Horizontal lines show the highest occupied molecular orbital of D and the lowest unoccupied molecular orbital of A, and 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 the ground and metastable states are shown by solid and dashed lines, respectively.

Figure 3

Temporal profiles of (a) $\rho \left(t\right)$ and (b) $u^{\prime }\left(t\right)$ are shown by solid lines when the A phase ionic ground state is excited by the half-cycle pulse with $ea{A}^{\left(\max \right)}=-2$. Horizontal dashed lines in (a) show the charge transfer $\overline{\rho }=0.751$ for the ionic ground state and $\overline{\rho }=0.227$ for the neutral ground state at the phase boundary. Horizontal dashed lines in (b) show the LOP $u_0^{\prime }=\pm 0.01$ for the ionic ground state and $u_0^{\prime }=0$ for the neutral ground state, and vertical dashed lines in (b) indicate the times when $u^{\prime }\left(t\right)=0$ holds and those when $u^{\prime }\left(t\right)$ exhibits local maxima or local minima.

Figure 4

Temporal profiles of (a) $\rho \left(t\right)$ and (b) $u^{\prime }\left(t\right)$ are shown by the solid lines when the A phase ionic ground state is excited by the half-cycle pulse with $ea{A}^{\left(\max \right)}=-2,-1$, 2, and 5. Horizontal dashed lines in (a) show the charge transfer $\overline{\rho }=0.751$ for the ionic ground state and $\overline{\rho }=0.227$ for the neutral ground state at the phase boundary. Horizontal dashed lines in (b) show the LOP $u_0^{\prime }=\pm 0.01$ for the ionic ground state and $u_0^{\prime }=0$ for the neutral ground state.

Figure 5

Temporal profiles of (a) $\rho \left(t\right)$, (b) $P_{\mathrm{el}}\left(t\right)-P_{\mathrm{el}}\left(t_0\right)$, (c) $I_1\left(t\right)-I_1\left(t_0\right)$ and $I_2\left(t\right)-I_2\left(t_0\right)$ with $t_0=4693.6$, and (d) $u^{\prime }\left(t\right)$ are shown by the solid lines when the A phase ionic ground state is excited by the double half-cycle pulses with $ea{A}^{\left(\max \right)}=-2$ and $t_{\mathrm{d}}=1900$. Horizontal dashed lines in (a) show the charge transfer $\overline{\rho }=0.751$ for the ionic ground state and $\overline{\rho }=0.227$ for the neutral ground state at the phase boundary. Horizontal dashed lines in (d) show the LOP $u_0^{\prime }=\pm 0.01$ for the ionic ground state and $u_0^{\prime }=0$ for the neutral ground state, and vertical dashed lines in (d) indicate times when $u^{\prime }\left(t\right)=0$ holds and those when $u^{\prime }\left(t\right)$ exhibits local maxima or local minima.

Figure 6

Temporal profiles of (a) $\rho \left(t\right)$ and (b) $u^{\prime }\left(t\right)$ are shown by the solid lines when the neutral ground state is excited by the half-cycle pulses with $ea{A}^{\left(\max \right)}=-2$. Horizontal dashed lines in (a) show the charge transfer $\overline{\rho }=0.751$ for the ionic ground state and $\overline{\rho }=0.227$ for the neutral ground state at the phase boundary. Horizontal dashed lines in (b) show the LOP $u_0^{\prime }=\pm 0.01$ for the ionic ground state and $u_0^{\prime }=0$ for the neutral ground state, and vertical dashed lines in (b) indicate the times when $u^{\prime }\left(t\right)=0$ holds and those when $u^{\prime }\left(t\right)$ exhibits local maxima or local minima.

Figure 7

Temporal profiles of (a) $\rho \left(t\right)$ and (b) $u^{\prime }\left(t\right)$ are shown by solid lines when the neutral ground state is excited by the half-cycle pulses with $ea{A}^{\left(\max \right)}=-2,-1,-0.5$, 0.5, 1, and 2. Horizontal dashed lines in (a) show the charge transfer $\overline{\rho }=0.751$ for the ionic ground state and $\overline{\rho }=0.227$ for the neutral ground state at the phase boundary. Horizontal dashed lines in (b) show the LOP $u_0^{\prime }=\pm 0.01$ for the ionic ground state and $u_0^{\prime }=0$ for the neutral ground state.

Figure 8

$|W_{\rho }(t,\omega )|$ for $ea{A}^{\left(\max \right)}=-2$ for the neutral ground state at the phase boundary. The frequency ${\omega }_{\mathrm{p}}\left(u^{\prime }\right)$ of the lowest in-gap peak versus time $t$ that satisfies the relation $u^{\prime }\left(t\right)=u^{\prime }$ is shown by dots at $u^{\prime }=\pm 0.00250,\pm 0.005,\pm 0.0075,\pm 0.01$, and $\pm 0.015$.

Figure 9

(a) Absorption spectrum ${\alpha }_0\left(\omega \right)$ and (b) ${\alpha }_0\left(\omega \right)$ in the in-gap region for the ground state $|{\varphi }_0\left(u^{\prime }\right)\rangle$ of the adiabatic Hamiltonian $H_{\mathrm{AP}}\left(u^{\prime }\right)$ for $u^{\prime }=0$, 0.0025, 0.005, 0.0075, 0.01, and 0.015 at ${\alpha }^{\prime }=0.143$.