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Motivated by the results of recent transport and optical conductivitystudies, we propose a semi-infinite two-dimensional lattice model forinteracting massive Dirac electrons in the pressurized organic conductor$\alpha$-(BEDT-TTF)$_2$I$_3$, and address the problem of domain wallconductivity in a charge-ordered insulating phase under realistic experimentalconditions. Using the extended Hubbard model at a mean field level, we presentresults of extensive numerical studies around the critical region of the model,reporting on the resistivity and optical conductivity calculated by means ofthe Nakano-Kubo formula. We find that the activation gap extracted from theresistivity data can be much smaller than the optical gap in the criticalregion, which is induced by metallic conduction along an one-dimensional domainwall emerging at the border of two charge-ordered ferroelectric regions withopposite polarizations. The data are consistent with the observed transport gapin real $\alpha$-(BEDT-TTF)$_2$I$_3$ samples that is reduced remarkably fasterthan the optical gap upon suppressing charge order with pressure. Our opticalconductivity also reveals an additional shoulder-like structure at low energyinside the gap, which is argued to be directly relevant to the metallic boundstates residing on the domain wall.

physical review. b./physical review. b

Domain Wall Conductivity with strong Coulomb interaction of  two-dimensional massive Dirac Electrons in the Organic Conductor  $\alpha$-(BEDT-TTF)$_2$I$_3$