Photoinduced melting of charge order in a quarter-filled electron system coupled with different types of phonons

Photoinduced melting of charge order is calculated by using the exact many-electron wave function coupled with classically treated phonons in the one-dimensional quarter-filled Hubbard model with Peierls and Holstein types of electron-phonon couplings. The model parameters are taken from recent experiments on ${\left(\mathrm{EDO}\text{−}\mathrm{TTF}\right)}_2{\mathrm{PF}}_6$ $(\mathrm{EDO}\text{−}\mathrm{TTF}=\text{ethylenedioxy}\text{–}\text{tetrathiafulvalene})$ with a (0110) charge order, where transfer integrals are modulated by molecular displacements (bond-coupled phonons) and site energies by molecular deformations (charge-coupled phonons). The charge-transfer photoexcitation from (0110) to (0200) configurations and that from (0110) to (1010) configurations have different energies. The corresponding excited states have different shapes of adiabatic potentials as a function of these two phonon amplitudes. The adiabatic potentials are shown to be useful in understanding differences in the photoinduced charge dynamics and the efficiency of melting, which depend not only on the excitation energy but also on the relative phonon frequency of the bond- and charge-coupled phonons.

Figure 1

(Color online) (a) Optical conductivity in (0110) ground state with 12 sites. Schematic charge distribution (circles) and deformation-induced potential (line) for the (b) (0110) ground state, (c) (1010) photoexcited state, and (d) (0200) photoexcited state. (e), (f), and (g) are their adiabatic potentials as a function of amplitudes of bond $\left(u_0\right)$- and charge $\left(v_0\right)$-coupled phonons.

Figure 2

(Color online) Time dependence of charge densities (a), (b), and (c) on short, intermediate, and long time scales, respectively, for excitation energy ${\omega }_{\mathrm{ext}}=1.5$ close to ${\omega }_{0200}$, $N_{\mathrm{ext}}=50$, and $E_{\mathrm{ext}}=0.340$ just below the threshold level for ${\omega }_{\alpha }={\omega }_{\beta }=0.02$.

Figure 3

(Color online) Reduction in charge order averaged over the period of oscillation at $t⩽4000$, as a function of increment in total energy, for (a) ${\omega }_{\mathrm{ext}}=0.5$, $N_{\mathrm{ext}}=17$, (b) ${\omega }_{\mathrm{ext}}=0.8$, $N_{\mathrm{ext}}=27$, and (c) ${\omega }_{\mathrm{ext}}=1.5$, $N_{\mathrm{ext}}=50$. Bare phonon frequencies are $({\omega }_{\alpha },{\omega }_{\beta })=(0.02,0.02)$ (black), (0.02, 0.005) (red), (0.06, 0.02) (magenta), (0.005, 0.02) (green), and (0.02, 0.06) (blue). The arrows show the lower limit required for the melting explained in the text.

Figure 4

(Color online) Time dependence of charge densities for ${\omega }_{\alpha }=0.02$ and ${\omega }_{\beta }=0.06$. Photoexcitations are (a) ${\omega }_{\mathrm{ext}}=0.5$ close to ${\omega }_{1010}$, $N_{\mathrm{ext}}=17$, and $E_{\mathrm{ext}}=0.030$ and (b) ${\omega }_{\mathrm{ext}}=1.5$ close to ${\omega }_{0200}$, $N_{\mathrm{ext}}=50$, and $E_{\mathrm{ext}}=0.280$.

Figure 5

(Color online) Time dependence of charge densities for ${\omega }_{\alpha }=0.06$ and ${\omega }_{\beta }=0.02$. Photoexcitations are (a) ${\omega }_{\mathrm{ext}}=0.5$ close to ${\omega }_{1010}$, $N_{\mathrm{ext}}=17$, and $E_{\mathrm{ext}}=0.032$ and (b) ${\omega }_{\mathrm{ext}}=1.5$ close to ${\omega }_{0200}$, $N_{\mathrm{ext}}=50$, and $E_{\mathrm{ext}}=0.310$.