Linear and nonlinear resonant tunneling through a minimal-size resonant structure in quantum molecular wires

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Abstract
Electron tunneling in a molecular wire with defects of the type ...AAABAAA..., where electronic states of molecules, host (A) and guest, at different sites are coupled via resonant interaction, is investigated. The model described by a simple Hamiltonian in the tight-binding representation bears at the same time a close resemblance to a double-barrier resonant heterostructure. Resonant tunneling is considered in the presence of an external electric field with the Hubbard electron-electron interaction at the guest site included. A closed set of equations, which accounts for the feedback between the current density in the wire and the resonance-state energy, is derived and used for calculations of the transmission coefficient of tunneling through defect. The latter determines the wire conductance of a completely degenerate Fermi gas. In the linear version of the theory presented, the Sautet-Joachim result is rederived. With nonlinear effects taken into account, we come to a self-consistent equation coinciding formally with that of the Davydov-Ermakov phenomenological model of bistable tunneling in double-barrier structures. In both studies the external field was absent, and thus, with its inclusion, an important generalization of the previous results is made. In the linear case (small current densities), an analytic expression of the wire-conductance field dependence is obtained and investigated. In the nonlinear case, the bistable regime of tunneling is shown to be operative, resulting in a specific behavior of the current response to the applied field. This behavior, i.e., the place of the hysteresis loop in the I-V curve, its form, and the loop number, correlates strongly with microscopic details of the resonant structure. An analysis of possible manifestations of bistability under varying magnitude of the applied bias constitutes the main result of the paper.