Non Equilibrium Green's Functions for Dummies: Introduction to the One Particle NEGF equations

TL;DR

This paper introduces the NEGF equations used for calculating current and charge densities in nanoscale conductors, providing a clear tutorial on their derivation and application, especially for ballistic and inelastic scattering regimes.

Contribution

It offers a simplified, accessible derivation and explanation of the NEGF equations, making this complex method more understandable for newcomers.

Findings

Derivation of NEGF equations for current and charge density

Explanation of NEGF application to ballistic conduction

Extension of NEGF to include inelastic scattering

Abstract

Non equilibrium Green's function methods are regularly used to calculate current and charge densities in nanoscale (both molecular and semiconductor) conductors under bias. This method is mainly used for ballistic conduction but may be extended to include inelastic scattering. In this tutorial paper the NEGF equations for the current and charge density matrix are derived and explained in a hopefully clear way.