Subgap tunneling through channels of polarons and bipolarons in chain conductors

We suggest a theory of internal coherent tunneling in the pseudogap region where the applied voltage is below the free electron gap. We consider quasi-one-dimensional (1D) systems where the gap is originated by a lattice dimerization (Peierls or SSH effect) as in polyacethylene, as well as low symmetry 1D semiconductors. Results may be applied to several types of conjugated polymers, to semiconducting nanotubes, and to quantum wires of semiconductors. The approach may be generalized to tunneling in strongly correlated systems showing the pseudogap effect, as in the family of high-${T}_{c}$ materials in the undoped limit. We demonstrate the evolution of tunneling current-voltage characteristics from smearing the free electron gap down to threshold for tunneling of polarons and further down to the region of bielectronic tunneling via bipolarons or kink pairs. The interchain tunneling is described in a parallel comparison with the on chain optical absorption, also within the subgap region.