Project title: Quantum effects of electronic transport on atomic dynamics in molecular junctions and organic semiconductors

Supervisors: Prof Lev Kantorovich and Prof Angus MacKinnon

Project description:

Recent work on the application of the Nonequilibrium Green’s Function (NEGF) formalism to electron transport in molecular junctions has made it possible to study the short-time transient in the current response to the sudden switch-on of a bias in the leads connected to the molecule [1]. This approach involves the solution of the Kadanoff-Baym (KB) equations for the Green’s function (GF) components of the embedded central region of the junction, where the system is evolved along a Konstantinov-Perel’ (KP) contour consisting of two horizontal branches and a vertical branch in the complex time plane. It also lends itself to a so-called partition-free approach [2].

Neglecting interactions, and working within the wide-band limit approximation (WBLA), an exact expression for the current was presented in [1] for the case of a static bias. We have generalized this result to obtain an analytic formula for the current response to an arbitrary time-dependent bias in the leads. As an intermediate step in this work, we have solved the KB equations to obtain the lesser GF of the central region as a function of two times. The dependence of the current on the preparation of the system may be studied by considering the time evolution of certain convolution integrals taken along the vertical part of the KP contour. The long-time dynamics of the current may be studied by pushing the switch-on time tback to negative infinity. In this limit, our result reduces to a known formula for the long-time current response to a time-dependent bias [3].

To illustrate the power of this formalism, we discuss its application to a single-level quantum dot with an AC bias on the leads. Transients, long-time dynamics, and ‘ringing’ oscillations in the current can now all be studied simultaneously.

We have also found a way to extend this approach to the calculation of a two-time current correlation function, describing the intrinsic noise on the current signal when the bias is allowed to vary arbitrarily with time. Our generalized theory reduces to well-known results for the shot and thermal noise under specific limiting conditions.         


[1]    G. Stefanucci and R. van Leeuwen (2013): Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction, CUP
[2]    G. Stefanucci and C. O. Almbladh (2004): Physical Review B, 69(19), 195318
[3]     A-P. Jauho, N. S. Wingreen and Y. Meir (2004): Physical Review B, 50(8), 5528