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 poly(G)-poly(C) DNA oligomers. In particular, our model provides a correct description of the molecular resonances which determine the quasi-linear part of the current out of the gap region.
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