To elucidate the different photoinduced melting dynamics of charge orders observed in the quasi-twodimensional organic conductors θ-(BEDT-TTF) 2RbZn(SCN)4 and α-(BEDT-TTF)2I 3 [BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene], we theoretically study the photoinduced time evolution of charge and spin correlation functions on the basis of exact many-electron wave functions coupled with classical phonons in extended Peierls-Hubbard models on anisotropic triangular lattices. In both salts, the so-called horizontal-stripe charge order is stabilized by nearest-neighbor repulsive interactions and electron-lattice interactions. In θ-(BEDT-TTF)2RbZn(SCN)4 (abbreviated as θ-RbZn), the stabilization energy due to lattice distortion is larger, so that a larger quantity of energy needs to be absorbed to melt charge and lattice orders. The photoinduced charge dynamics shows a complex behavior owing to a substantial number of nearly degenerate eigenstates involved. This is related to the high structural symmetry when the lattice is undistorted. In α-(BEDT-TTF)2I3 (abbreviated as α-I3), the lattice stabilization energy is smaller, and a small quantity of energy is sufficient to melt charge and lattice orders leading to a metallic phase. The photoinduced charge dynamics shows a sinusoidal oscillation. In-I3, the low structural symmetry ensures nearly spin-singlet bonds between hole-rich sites, where the spin correlation survives even after photoexcitation.
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