The current-voltage characteristics and charge distribution of charge-ordered electron systems at quarter-filling under an applied bias voltage (V) are investigated theoretically by using nonequilibrium Green's functions. We consider an extended Hubbard model with long-range Coulomb interactions on a square lattice, which describes a checkerboard-type charge order in the absence of the bias V. The effects of metallic electrodes are incorporated into the self-energy. The electron density and a scalar potential that satisfies the Poisson equation with a suitable boundary condition are calculated self-consistently within the Hartree approximation. A first-order transition is observed from the charge-ordered insulating state to a conductive state with increasing V. In the former state, the charge distribution is almost unchanged by V, whereas the charge order disappears so that the charge distribution is basically uniform in the latter state.
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