Single molecule bridge as a testing ground for using NGF outside of the steady current regime

The simplest nanoscopic system, a molecular bridge consisting of a molecular island with one or few electronic or vibronic levels coupled to non-interacting leads can be treated using non-equilibrium Green's functions (NGF). We follow the well known procedure of Jauho, Wingreen and Meir (JWM). In the present work, we concentrate on the little investigated transient behavior of the molecular bridge undergoing abrupt changes. The transient process depends on the initial conditions at a finite time which may incorporate initial correlations. As an example, we study the electron response to sudden connecting the molecule to one or both leads. To obtain explicit solutions, we neglect all interactions at the island, whose role is mimicked by the island–leads coupling. We explore this analogy and obtain a complete solution for the transient NGF for arbitrary “initial correlations” represented by off-diagonal coherences between the initial electron state of the island and of the leads. This direct one-electron solution is confronted with the field theoretic approach in the particular case of the switch-on states, for which the initial correlations result from the previous history of the system. This is formally captured by the partitioning-in-time of the NGF, which we combine with the JWM theory. It is the virtue of partitioning method to express the transient NGF in terms of the building blocks of stationary-state NGF with zero, one or both leads connected. The direct and the partitioning solutions are reduced explicitly from one to the other, clarifying thus the meaning of the singular terms of the self-energy for correlated initial conditions.