Dynamical Phase Transitions in the Photodriven Charge-Ordered Dirac-Electron System

We study photoinduced phase transitions and charge dynamics in the interacting Dirac-electron system with a charge-ordered ground state theoretically by taking an organic salt $\alpha \text{−}{(\text{BEDT-TTF})}_2{\mathrm{I}}_3$. By analyzing the extended Hubbard model for this compound using a combined method of numerical simulations based on the time-dependent Schrödinger equation and the Floquet theory, we observe successive dynamical phase transitions from the charge-ordered insulator to a gapless Dirac semimetal and, eventually, to a Chern insulator phase under irradiation with circularly polarized light. These phase transitions occur as a consequence of two major effects of circularly polarized light, i.e., closing of the charge gap through melting the charge order and opening of the topological gap by breaking the time-reversal symmetry at the Dirac points. We demonstrate that these photoinduced phenomena are governed by charge dynamics of driven correlated Dirac electrons.

Figure 1

(a) Conduction layer of $\alpha \text{−}{(\text{BEDT-TTF})}_2{\mathrm{I}}_3$. The ellipses represent the BEDT-TTF molecules, and the gray rectangle indicates the unit cell that contains four molecules ($A$, $A^{\prime }$, $B$, and $C$). In the charge-ordered phase, the sites $A^{\prime }$ and $C$ are electron rich, whereas the sites $A$ and $B$ are electron poor. (b) Schematic illustration of the photoirradiation on charge-ordered $\alpha \text{−}{(\text{BEDT-TTF})}_2{\mathrm{I}}_3$ with circularly polarized light. The shaded and open ellipses represent the charge disproportionation. (c) Dispersion relations of bands above and below the Fermi level for the charge-ordered phase.

Figure 2

(a)–(c) Time evolutions of electron densities $⟨n_{\alpha }⟩$ at four molecular sites ($\alpha =A$, $A^{\prime }$, $B$, and $C$) for various light intensities, i.e., (a) $E^{\omega }=1.4$, (b) $E^{\omega }=5.6$, and (c) $E^{\omega }=11.2\mathrm{MV}/\mathrm{cm}$, when the light frequency is $\hslash \omega =0.7\mathrm{eV}$. The bold solid lines present the results after the high-frequency components are filtered out. Time profiles of the light amplitude $|\mathit{E}(\tau )|$ are also depicted by dashed lines. (d)–(f) Corresponding projected band dispersions of the transient states.

Figure 3

Calculated dispersion relations (dashed lines) of the Floquet bands ${ϵ}_{n,\lambda }(\mathit{k})$ along the ($k_x$, $k_y^{D1}$) line (lower panels), and those along the ($k_x$, $k_y^{D2}$) line around the Fermi level (upper panels) for various light amplitudes, i.e., (a) $E^{\omega }=1.4$, (b) $E^{\omega }=5.6$, and (c) $E^{\omega }=11.2\mathrm{MV}/\mathrm{cm}$. We depict $A_{\mathit{k}}(ϵ,{\tau }_{\mathrm{pr}})$ for comparison. These light amplitudes correspond to the photoinduced phases of (a) the charge-ordered insulator, (b) the Dirac semimetal, and (c) the Chern insulator, as argued shortly. Here the momentum $k_y^{D1}$ ($k_y^{D2}$) is fixed at a constant value such that the line runs over the Dirac point located in the area of $k_x<\pi$ ($k_x>\pi$).

Figure 4

$E^{\omega }$ dependence of (a) two gaps ${\mathrm{\Delta }}_1$ and ${\mathrm{\Delta }}_2$ at the Dirac points and (b) Chern number $N_{\text{Ch}}$ in the insulator phases when $\hslash \omega =0.7\mathrm{eV}$.