Real-space description of current-constrained molecular junctions

Abstract

A current constrained approach is proposed for the calculation of characteristic current/voltage curves for molecular junctions described in a real space representation. A steady-state current is imposed on the molecule prepared in a nonequilibrium state, and the voltage drop is obtained from the electrical power spent on the molecule to sustain the current. The molecular resistance is related to relaxation phenomena that drive the molecule towards the equilibrium state. A phenomenological model, borrowed from the field of molecular spectroscopy, is adopted to describe relaxation, accounting for both depopulation and dephasing (inelastic and elastic scattering). The current is related to coherences, and the coherence lifetimes, with contributions from both depopulation and dephasing, enter the definition of the molecular resistance. For the specific case of a single electron in a two-site junction the standard result of conductivity quantization is regained, a result that holds for dispersionless as well as dispersive junctions. The proper implementation of the continuity constraint for steady-state dc transport requires the introduction of multiple Lagrange multipliers and results in nonlinear potential profiles across the molecule leading to the intriguing concept of bond resistance.