A non-equilibrium equation-of-motion approach to quantum transport utilizing projection operators

TL;DR

This paper introduces a projection operator-based non-equilibrium Green function method for quantum transport, resolving truncation issues and ensuring symmetry, with practical schemes and numerical validation against existing techniques.

Contribution

It reformulates Tserkovnikov's equilibrium approach for non-equilibrium quantum transport, providing a canonical EOM form and a practical simulation scheme.

Findings

The method prevents symmetry violations in truncated EOMs.

Numerical results agree well with exact solutions and other techniques.

The approach effectively handles time-dependent non-equilibrium situations.

Abstract

We consider a projection operator approach to the non-equilbrium Green function equation-of-motion (PO-NEGF EOM) method. The technique resolves problems of arbitrariness in truncation of an infinite chain of EOMs, and prevents violation of symmetry relations resulting from the truncation. The approach, originally developed by Tserkovnikov [Theor. Math. Phys. 118, 85 (1999)] for equilibrium systems, is reformulated to be applicable to time-dependent non-equilibrium situations. We derive a canonical form of EOMs, thus explicitly demonstrating a proper result for the non-equilibrium atomic limit in junction problems. A simple practical scheme applicable to quantum transport simulations is formulated. We perform numerical simulations within simple models, and compare results of the approach to other techniques, and (where available) also to exact results.