Transmission through a defect in polyacene: the extreme limit of ultra narrow graphene

We compute the transmission of an electron through an impurity in polyacene. An analytical expression for the transmission coefficient is found. For simplicity the disorder is confined to a single unit cell, but the generalization to several unit cells is straightforward. Both on-site and off-diagonal defects are considered. When the impurity preserves the inversion symmetry around the central axis, the scattering problem can be reduced to that of two independent chains with an alternating sequence of two types of atoms.