Exact relations for the differential conductance and rectification ratio of the tunnel current in the redox-mediated tunneling junctions and demonstration within the fully diabatic approximation for electron transitions

Abstract

Exact relations for the differential conductance and rectification ratio of the tunnel current through a single one-level redox-active molecule in the electrochemical metal-molecular-metal tunneling junction are obtained in the wide-band approximation. These relations are valid at any temperatures, strengths of the redox molecule-electrodes coupling, arbitrary interaction of the valence electrons with arbitrary phonon modes, arbitrary positions of the redox-molecule valence level and any energies of the Coulomb repulsion U between electrons at the valence level. These relations have the particular physical importance because they permit to reveal in the general form the parameters which determine values of the differential conductance and rectification ratio. The obtained relations also permit to consider the differential conductance/overpotential and rectification ratio/overpotential characteristics only in the specific regions of the parameter space. In order to demonstrate the obtained relations, we calculate and interpret the differential conductance/overpotential and rectification ratio/overpotential characteristics for the case when the redox-mediated tunneling junction has only the classical phonon modes and is described within the fully diabatic approximation.