Backbone-induced semiconducting behavior in short $\mathrm{DNA}$ wires

We propose a model Hamiltonian for describing charge transport through short homogeneous double stranded DNA molecules. We show that the hybridization of the overlapping $\pi$ orbitals in the base-pair stack coupled to the backbone is sufficient to predict the existence of a gap in the nonequilibrium current-voltage characteristics with a minimal number of parameters. Our results are in a good agreement with the recent finding of semiconducting behavior in short $\mathrm{poly}\mathrm{}\left(G\right)\mathrm{}$-$\mathrm{poly}\mathrm{}\left(C\right)\mathrm{}$ DNA oligomers. In particular, our model provides a correct description of the molecular resonances which determine the quasilinear part of the current out of the gap region.