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The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include…
Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms requires the tight-binding Hamiltonian to be in the form of a block-tridiagonal matrix. Here, we…
The Hierarchical Schur Complement method (HSC), and the HSC-extension, have significantly accelerated the evaluation of the retarded Green's function, particularly the lesser Green's function, for two-dimensional nanoscale devices. In this…
Non-equilibrium electronic quantum transport is crucial for the operation of existing and envisioned electronic, optoelectronic, and spintronic devices. The ultimate goal of encompassing atomistic to mesoscopic length scales in the same…
In this thesis we showed that Non-equilibrium Green's Function Perturbation Theory (NEGF) is really the overarching perturbative transport theory. This is shown in great detail by using NEGF as a starting point and developing in 3…
Based on the non-equilibrium Green's function (NEGF) coupled with density function theory (DFT), namely, NEGF-DFT quantum transport theory, we propose an efficient formalism to calculate the transient current of molecular devices under a…
The concept of transmission eigenchannels is described in a tight-binding nonequilibrium Green's function (NEGF) framework. A simple procedure for calculating the eigenchannels is derived using only the properties of the device subspace and…
A self-consistent method for calculating electron transport through a molecular device is proposed. It is based on density functional theory electronic structure calculations under periodic boundary conditions and implemented in the…
In this colloquia review we discuss methods for thermal transport calculations for nanojunctions connected to two semi-infinite leads served as heat-baths. Our emphases are on fundamental quantum theory and atomistic models. We begin with…
The nonequilibrium Green's function (NEGF) formalism is a powerful tool to study the nonequilibrium dynamics of correlated lattice systems, but its applicability to realistic system sizes and long timescales is limited by unfavorable memory…
Quantum transport through single molecules is very sensitive to the strength of the molecule-electrode contact. Here, we investigate the behavior of a model molecular junction weakly coupled to external electrodes in the case where charging…
{\it Ab initio} computational methods for electronic transport in nanoscaled systems are an invaluable tool for the design of quantum devices. We have developed a flexible and efficient algorithm for evaluating $I$-$V$ characteristics of…
We present a generalized approach for computing electron conductance and I-V characteristics in multiterminal junctions from first-principles. Within the framework of Keldysh theory, electron transmission is evaluated employing an O(N)…
Driven by Moore's Law, the dimensions of transistors have been pushed down to the nanometer scale. Advanced quantum transport (QT) solvers are required to accurately simulate such nano-devices. The non-equilibrium Green's function (NEGF)…
We derive a general expression for the electron nonequilibrium (NE) distribution function in the context of steady state quantum transport through a two-terminal nanodevice with interaction. The central idea for the use of NE distributions…
We demonstrate an efficient nonequilibrium Green's function transport calculation procedure based on the real-space finite-difference method. The direct inversion of matrices for obtaining the self-energy terms of electrodes is…
Electrical conduction through a two-terminal molecular device is studied using non-equilibrium Green's functions (NEGF) formalism. Such junction is made of a short linear wire which is connected to the metallic electrodes. Molecule itself…
Transport in molecular electronic devices is different from that in semiconductor mesoscopic devices in two important aspects: (1) the effect of the electronic structure and (2) the effect of the interface to the external contact. A…
We review the description and modeling of transport phenomena among the electron systems coupled via scalar or vector photons. It consists of three parts. The first part is about scalar photons, i.e., Coulomb interactions. The second part…
Inelastic effects in electron transport through nano-sized devices are addressed with a method based on nonequilibrium Green's functions (NEGF) and perturbation theory to infinite order in the electron-vibration coupling. We discuss the…