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 computationally demanding in the real-space method because the matrix dimension corresponds to the number of grid points in the unit cell of electrodes, which is much larger than that of sites in the tight-binding approach. The procedure using the ratio matrices of the overbridging boundary-matching technique [Y. Fujimoto and K. Hirose, Phys. Rev. B 67, 195315 (2003)], which is related to the wave functions of a couple of grid planes in the matching regions, greatly reduces the computational effort to calculate self-energy terms without losing mathematical strictness. In addition, the present procedure saves computational time to obtain the Green's function of the semi-infinite system required in the Landauer-Büttiker formula. Moreover, the compact expression to relate Green's functions and scattering wave functions, which provide a real-space picture of the scattering process, is introduced. An example of the calculated results is given for the transport property of the BN ring connected to (9,0) carbon nanotubes. The wave-function matching at the interface reveals that the rotational symmetry of wave functions with respect to the tube axis plays an important role in electron transport. Since the states coming from and going to electrodes show threefold rotational symmetry, the states in the vicinity of the Fermi level, the wave function of which exhibits fivefold symmetry, do not contribute to the electron transport through the BN ring.

We present a first-principles study of the electron conduction properties of single-row nanowires suspended between semi-infinite electrodes. The single-row sodium nanowires exhibit conductance oscillation and bunching of high electron density with two atom lengths in the channel density distribution. The relationship between the period of the conductance oscillation and the length of the bunches is interpreted using a simplified model. The difference in the penetration parameters between the incident Bloch wave and the reflected one inside the nanowire is closely related to the period of the conductance oscillation and the length of the bunches.

We present a time-saving simulator within the framework of the density functional theory to calculate the transport properties of electrons through nanostructures suspended between semi-infinite electrodes. By introducing the Fourier transform and preconditioning conjugate-gradient algorithms into the simulator, a highly efficient performance can be achieved in determining scattering wave functions and electron-transport properties of nanostructures suspended between semi-infinite jellium electrodes. To demonstrate the performance of the present algorithms, we study the conductance of metallic nanowires and the origin of the oscillatory behavior in the conductance of an Ir nanowire. It is confirmed that the s-d(z²) channel of the Ir nanowire exhibits the transmission oscillation with a period of two-atom length, which is also dominant in the experimentally obtained conductance trace.

We present first-principles calculations of electron conduction properties of monatomic sodium wires suspended between semi-infinite crystalline electrodes, using the overbridging boundary-matching method. We find that the conductances oscillate depending on the number of atoms in the wire, N atom . Furthermore, the values of conductances are $3 G 0 (G 0 = 2e 2 =h) for the closed packed structure and $1 G 0 for singlerow wires, which is in agreement with the experimental results of the conductance histogram.

The spin relaxation due to the spin-orbit interaction (SOI) is studied theoretically in a quantum well with electrons occupying only the ground subband. First, it is shown that the coefficient of the Rashba SOI is proportional to b off − 1, in which the parameter b off , determined by the band offsets and the band gaps, passes through unity, for example, by changing x in Ga 0.47 In 0.53 As(well)/Al x Ga 1−x As y Sb 1−y (barrier). Second, it is derived that the transition matrix element of each spin-flip phonon scattering has the same proportionality factor b off − 1, in addition to the impurity scattering previously studied by the same authors [Phys. Rev. B 89, 075314 (2014)]. These findings suggest the possibility of strongly suppressing the spin-relaxation rate by choosing appropriate materials.