Quantum Transport Simulations of Nano-systems: An Introduction to the Green’s Function Approach

In this chapter we present a detailed treatment of coherent charge transport at the nano-scale. To begin with, we explain the Landauer-Buttiker theory and its underlaying assumptions. Then we introduce the non-equilibrium Green’s function (NEGF) technique, which provides a powerful framework to implement the theory for real device simulations and to extend it beyond linear response. The goal of the first part of the chapter is to provide the reader with the basic knowledge required to understand and implement a NEGF-based computational scheme for non-interacting tight-binding models. The second part of the chapter illustrates how NEGF can be combined with density functional theory (DFT) to carry out first-principles simulations of nanoscale devices. We provide guidelines that will allow the reader to perform practical DFT+NEGF simulations by using the most common implementations available in electronic structure software.