## 4 Photoinduced Dynamics
### Melting of Hexagrams  
Now, we further increase the laser amplitude and see how the lattice dynamics changes. Figure 7 shows the dynamics of the charge densities averaged over A, B, and C sites for the larger peak amplitudes \(E_{0}=4.61\) and \(23.1\) MV/cm in panels (a,b), respectively. For \(E_{0}=4.61\) MV/cm, the CDW order decreases by \(\sim\!20\)%, which is much enhanced than the case of \(E_{0}=0.92\) MV/cm shown in Figure 5. For \(E_{0}=23.1\) MV/cm, the CDW order disappears and the charge distribution becomes nearly uniform within \(\sim\!20\) fs. We note that the PLD remains present on this time scale as shown in panel (c). Only the CDW order of the hexagram shape melts down on the short time scale.  
Next, we discuss the energy efficiency of the photoinduced CDW melting. We have calculated the energy absorption \(\Delta E_{\rm abs}\equiv E(t=0\,{\rm fs})-E_{\rm init}\), and obtained \(\Delta E_{\rm abs}=4.6\) and \(39\) eV per two hexagrams for \(E_{0}=4.61\) and \(23.1\) MV/cm, respectively. We compare these values with the energy difference \(\Delta E_{\rm CDW}\equiv E_{\rm uniform}-E_{\rm init}\). Here, \(E_{\rm uniform}\) denotes the energy of a virtual uniform state and is defined as the expectation value of \(\hat{H}_{\rm total}\) (8) at \(x=-1.5\) calculated for the electronic ground state of \(\hat{H}_{\rm total}\) for \(x=0\). We obtain \(\Delta E_{\rm CDW}=5.8\) eV per two hexagrams, and it is an estimate of the energy needed to wash out the CDW order without deforming the PLD. It is consistent with the fact that \(\Delta E_{\rm abs}<\Delta E_{\rm CDW}\) for \(E_{0}=4.61\) MV/cm, where the CDW is suppressed but remains, whereas \(\Delta E_{\rm abs}>\Delta E_{\rm CDW}=0.15\Delta E_{\rm abs}\) for \(E_{0}=23.1\) MV/cm, where the CDW melts down. Thus, 15% of the absorbed energy is used for the CDW melting, and the remaining 85% is converted into heat.  
Figure 6: (**a**) time profile of lattice distortion \(x(t)\) (solid) and its sinusoidal fitting (dashed); (**b**) schematic illustration of mechanism of lattice dynamics \(x(t)\).  
To melt the CDW order, the laser-electron interaction is not the only way since the lattice motion is involved on the long time scale. We show the lattice dynamics in Figure 7 for some strong laser fields. For \(E_{0}=4.61\,\mathrm{MV/cm}\), \(x(t)\) hits zero, meaning that the PLD of the hexagram shape melts down and the CDW order of electrons thereby disappears. We note that this field amplitude is not strong enough to completely melt the CDW order on the short time scale. However, in the long run, the laser energy absorbed by the electrons is transferred to the lattice motion, which affects the charge density through the electron-lattice coupling. On the long time scale, the electron-lattice cooperative dynamics becomes more important.  
These electron-lattice dynamics are quite different from those found in experimental [43] and theoretical studies [44; 45] on charge order melting in quasi-two-dimensional organic conductors. In these materials, the charge order is mainly produced by long-range Coulomb repulsion and weakly assisted by an electron-lattice coupling. Thus, the charge order can be melted efficiently by a pulse laser with little changing the lattice distortion. See also [46] for the efficiency of the charge order melting in a quasi-one-dimensional organic conductor.