We theoretically investigate charge order and nonlinear conduction in the quasi-two-dimensional organic conductor β-(meso-DMBEDT-TTF) 2PF6 (DMBEDT-TTF=dimethylbis(ethylenedithio) tetrathiafulvalene). Within the Hartree-Fock approximation, we study the effects of structural distortion on the experimentally observed checkerboard charge order and its bias-induced melting by using an extended Hubbard model with Peierls- and Holstein-types of electron-lattice interactions. The structural distortion is important in realizing the charge order. The current-voltage characteristics obtained by a nonequilibrium Green's function method indicate that a charge-ordered insulating state changes into a conductive state. Although the charge order and lattice distortions are largely suppressed at a threshold voltage, they remain finite even in the conductive state. We discuss the relevance of the results to experimental observations, especially to a possible bias-induced metastable state.
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