Charge ordering (CO) with long periods in a geometrically frustrated system, θ-(BEDT-TTF)2X, is numerically studied. We consider interacting fermion models on an anisotropic triangular lattice: the extended Hubbard model and spinless fermion model, taking account of inter-site Coulomb interactions on not only the nearest-neighbor (NN) bonds but also next-nearest-neighbor (NNN) bonds. By applying the Lanczos exact diagonalization method, we find that long-period charge correlations become dominant when NNN terms are included in the charge-frustrated region. The calculated optical excitation spectra show that the charge transfer excitations in the long-period CO extend to a lower energy range than those in the short-period CO states including the 3-fold CO stabilized when NNN terms are absent. Our results suggest that the charge correlations experimentally observed in the title compounds near the CO insulating phase can be viewed as a tendency toward a "tilted stripe"-type CO with large charge fluctuations.
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