Nonequilibrium diagram technique and its application to study quantum electron transport in nanoelectronic devices

Abstract

This work gives an overview of the non-equilibrium Green function (NEGF) technique in quantum field theory by using Langreth's method. The difference between the diagrammatic Green function (GF) technique for equilibrium and nonequilibrium systems is discussed with respect to Keldysh contour. A short review of the diagrammatic technique for an equilibrium system is presented for various types of interactions that are possible in nanoelectronic devices such as external field, electron-electron interaction, and electron-Boson interaction. Moreover, the random phase approximation (RPA) and Hedin's equation are reviewed with the presence of electron-electron interaction and electron-Boson interaction. Based on Langreth's rules, the Keldysh components of the first two orders of the T-matrix and self-energies, irreducible polarization, and vertex corrections in the presence of the electron-electron and electron-Boson interaction are extracted. The RPA and Hedin's equations are formed in Keldysh space in the presence of electron-electron interaction, and electron-Boson interaction. Finally, the application of the NEGF technique to analyze the quantum transport in nanoelectronic devices, i.e., electron transport in metal-insulator-metal tunneling junction, tunnelling resonances system, and nanostructure sensitized photovoltaic device, are discussed.