Nonlinear electronic transport in nanoscopic devices: Nonequilibrium Green's functions versus scattering approach

TL;DR

This paper compares the Nonequilibrium Green's function method with the scattering approach for analyzing nonlinear electronic transport in nanodevices, highlighting their relations, gauge invariance, and symmetry properties.

Contribution

It establishes a connection between NEGF and scattering approaches, extending conductance calculations to arbitrary order and analyzing gauge invariance and symmetry in nonlinear transport.

Findings

NEGF current is gauge invariant to all orders in voltage

Conductance coefficients exhibit specific symmetry properties under magnetic field inversion

Onsager reciprocity relations are violated at higher biases

Abstract

We study the nonlinear elastic quantum electronic transport properties of nanoscopic devices using the Nonequilibrium Green's function (NEGF) method. The Green's function method allows us to expand the $I-V$ characteristics of a given device to arbitrary powers of the applied voltages. By doing so, we are able to relate the NEGF method to the scattering approach, showing their similarities and differences and calculate the conductance coefficients to arbitrary order. We demonstrate that the electronic current given by NEGF is gauge invariant to all orders in powers of $V$, and discuss the requirements for gauge invariance in the standard Density Functional Theory (DFT) implementations in molecular electronics. We also analyze the symmetries of the nonlinear conductance coefficients with respect to a magnetic field inversion and the violation of the Onsager reciprocity relations with increasing source-drain bias.