This review deals with the nonequilibrium Green’s function (NEGF) method applied to the problems of energy transport due to atomic vibrations (phonons), primarily for small junction systems. We present a pedagogical introduction to the subject, deriving some of the well-known results such as the Laudauer-like formula for heat current in ballistic systems. The main aim of the review is to build the machinery of the method so that it can be applied to other situations, which are not directly treated here. In addition to the above, we consider a number of applications of NEGF, not in routine model system calculations, but in a few new aspects showing the power and usefulness of the formalism. In particular, we discuss the problems of multiple leads, coupled left-right-lead system, and system without a center. We also apply the method to the problem of full counting statistics. In the case of nonlinear systems, we make general comments on the thermal expansion effect, phonon relaxation time, and a certain class of mean-field approximations. Lastly, we examine the relationship between NEGF, reduced density matrix, and master equation approaches to thermal transport.

The rapid miniaturization of electronic devices motivates research interests in quantum transport. Recently time-dependent quantum transport has become an important research topic. Here we review recent progresses in the development of time-dependent density-functional theory for quantum transport including the theoretical foundation and numerical algorithms. In particular, the reducedsingle electron density matrix based hierarchical equation of motion, which can be derived from Liouville–von Neumann equation, is reviewed in details. The numerical implementation is discussed and simulation results of realistic devices will be given.

We review the recently developed three-dimensional (3D) atom-superposition approach for simulating scanning tunneling microscopy (STM) and spectroscopy (STS) based on ab initio electronic structure data. In the method, contributions from individual electron tunneling transitions between the tip apex atom and each of the sample surface atoms are summed up assuming the one-dimensional (1D) Wentzel–Kramers–Brillouin (WKB) approximation in all these transitions. This 3D WKB tunneling model is extremely suitable to simulate spin-polarized STM and STS on surfaces exhibiting a complex noncollinear magnetic structure, i.e., without a global spin quantization axis, at very low computational cost. The tip electronic structure from first principles can also be incorporated into the model, that is often assumed to be constant in energy in the vast majority of the related literature, which could lead to a misinterpretation of experimental findings. Using this approach, we highlight some of the electron tunneling features on a prototype frustrated hexagonal antiferromagnetic Cr monolayer on Ag(111) surface. We obtain useful theoretical insights into the simulated quantities that is expected to help the correct evaluation of experimental results. By extending the method to incorporate a simple orbital dependent electron tunneling transmission, we reinvestigate the bias voltage- and tip-dependent contrast inversion effect on theW(110) surface. STM images calculated using this orbital dependent model agree reasonably well with Tersoff-Hamann and Bardeen results. The computational efficiency of the model is remarkable as the k-point samplings of the surface and tip Brillouin zones do not affect the computational time, in contrast to the Bardeen method. In a certain case we obtain a relative computational time gain of 8500 compared to the Bardeen calculation, without the loss of quality. We discuss the advantages and limitations of the 3D WKB method, and show further ways to improve and extend it.

Carbon nanomaterials (CNMs) are prompting candidates for next generational electronics. In this review we provide a mini overview of recent results on the conductivity of carbon-based molecular junctions obtained from ab-initio methods. CNMs used as nanoelectrodes and molecular materials in molecular junctions are discussed. The functionalities that include the nanomechanically controlled molecular conductance switches, negative differential resistance devices, and electronic rectifiers realized by using CNMs have been demonstrated.

Topological insulators have a bulk band gap like an ordinary insulator and conducting states on their edge or surface which are formed by spin–orbit coupling and protected by time-reversal symmetry. We report theoretical analyses of the electronic properties of three-dimensional topological insulator Bi₂Se₃ film on different energies. We choose five different energies (–123, –75, 0, 180, 350 meV) around the Dirac cone (–113 meV). When energy is close to the Dirac cone, the properties of wave function match the topological insulator’s hallmark perfectly. When energy is far way from the Dirac cone, the hallmark of topological insulator is broken and the helical states disappear. The electronic properties of helical states are dug out from the calculation results. The spin-momentum locking of the helical states are confirmed. A 3-fold symmetry of the helical states in Brillouin zone is also revealed. The penetration depth of the helical states is two quintuple layers which can be identified from layer projection. The charge contribution on each quintuple layer depends on the energy, and has completely different behavior along K and M direction in Brillouin zone. From orbital projection, we can find that the maximum charge contribution of the helical states is p_z orbit and the charge contribution on p_yand p_x orbits have 2-fold symmetry.

We present first-principle calculations of electric and thermo spin transfer torques (STT) in Fe/Vacuum(Vac)/Fe magnetic tunnel junctions (MTJs). Our quantitative studies demonstrate rich bias dependence of STT and tunnel magneto resistance (TMR) behaviors with respect to the interface roughness. Thermoelectric effects in Fe/Vac/Fe MTJs is remarkable. We observe larger ZT of 6.2 in 8 ML clean Vacuum barrier, where the heavily restrained thermal conductance should be responsible for. Thermo-STT in Fe/Vac/Fe MTJs show same order as that in Fe/MgO/Fe MTJs with similar barrier thickness.

We theoretically investigate the electronic transport properties of a multi-terminal tetrahedronstructured DNA under a uniform magnetic field. Based on a tight-binding model, the current and nonlocal resistance are calculated under different situations by employing the Landauer–Büttiker formula. Our results indicate that the current displays a clear sign of interference in the presence of the magnetic field and can be mainly divided into three patterns, as demonstrated by the Fourier transformation. Furthermore, the tetrahedron-structured DNA can be used as a molecular switch. The underlying physical mechanisms are analyzed for the various phenomena observed in this threedimensional DNA interferometer.

We report theoretical investigations on the role of interfacial bonding mechanism and its resulting structures to quantum transport in molecular wires. Two bonding mechanisms for the Au-S bond in an Au(111)/1,4-benzenedithiol(BDT)/Au(111) junction were identified by ab initio calculation, confirmed by a recent experiment, which, we showed, critically control charge conduction. It was found, for Au/BDT/Aujunctions, the hydrogen atom, bound by a dative bond to the Sulfur, is energetically non-dissociativeafter the interface formation. The calculated conductance and junction breakdown forces of H-non-dissociative Au/BDT/Au devices are consistent with the experimental values, while the H-dissociated devices, with the interface governed by typical covalent bonding, give conductance more than an order of magnitude larger. By examining the scattering states that traverse the junctions, we have revealed that mechanical and electric properties of a junction have strong correlation with the bonding configuration. This work clearly demonstrates that the interfacial details, rather than previously believed many-body effects, is of vital importance for correctly predicting equilibrium conductance of molecular junctions; and manifests that the interfacial contact must be carefully understood for investigating quantum transport properties of molecular nanoelectronics.