Self-energy matrices for electron transport calculations within the real-space finite-difference formalism.

The self-energy term used in transport calculations, which describes the coupling between electrode and transition regions, is able to be evaluated only from a limited number of the propagating and evanescent waves of a bulk electrode. This obviously contributes toward the reduction of the computational expenses in transport calculations. In this paper, we present a mathematical formula for reducing the computational expenses further without using any approximation and without losing accuracy. So far, the self-energy term has been handled as a matrix with the same dimension as the Hamiltonian submatrix representing the interaction between an electrode and a transition region. In this work, through the singular-value decomposition of the submatrix, the self-energy matrix is handled as a smaller matrix, whose dimension is the rank number of the Hamiltonian submatrix. This procedure is practical in the case of using the pseudopotentials in a separable form, and the computational expenses for determining the self-energy matrix are reduced by 90% when employing a code based on the real-space finite-difference formalism and projector-augmented wave method. In addition, this technique is applicable to the transport calculations using atomic or localized basis sets. Adopting the self-energy matrices obtained from this procedure, we present the calculation of the electron transport properties of C_{20} molecular junctions. The application demonstrates that the electron transmissions are sensitive to the orientation of the molecule with respect to the electrode surface. In addition, channel decomposition of the scattering wave functions reveals that some unoccupied C_{20} molecular orbitals mainly contribute to the electron conduction through the molecular junction.

First-principles calculation method for electron transport based on the grid Lippmann-Schwinger equation.

We develop a first-principles electron-transport simulator based on the Lippmann-Schwinger (LS) equation within the framework of the real-space finite-difference scheme. In our fully real-space-based LS (grid LS) method, the ratio expression technique for the scattering wave functions and the Green's function elements of the reference system is employed to avoid numerical collapse. Furthermore, we present analytical expressions and/or prominent calculation procedures for the retarded Green's function, which are utilized in the grid LS approach. In order to demonstrate the performance of the grid LS method, we simulate the electron-transport properties of the semiconductor-oxide interfaces sandwiched between semi-infinite jellium electrodes. The results confirm that the leakage current through the (001)Si-SiO_{2} model becomes much larger when the dangling-bond state is induced by a defect in the oxygen layer, while that through the (001)Ge-GeO_{2} model is insensitive to the dangling bond state.

Real-space finite-difference calculation method of generalized Bloch wave functions and complex band structures with reduced computational cost.

Generalized Bloch wave functions of bulk structures, which are composed of not only propagating waves but also decaying and growing evanescent waves, are known to be essential for defining the open boundary conditions in the calculations of the electronic surface states and scattering wave functions of surface and junction structures. Electronic complex band structures being derived from the generalized Bloch wave functions are also essential for studying bound states of the surface and junction structures, which do not appear in conventional band structures. We present a novel calculation method to obtain the generalized Bloch wave functions of periodic bulk structures by solving a generalized eigenvalue problem, whose dimension is drastically reduced in comparison with the conventional generalized eigenvalue problem derived by Fujimoto and Hirose [Phys. Rev. B 67, 195315 (2003)]. The generalized eigenvalue problem derived in this work is even mathematically equivalent to the conventional one, and, thus, we reduce computational cost for solving the eigenvalue problem considerably without any approximation and losing the strictness of the formulations. To exhibit the performance of the present method, we demonstrate practical calculations of electronic complex band structures and electron transport properties of Al and Cu nanoscale systems. Moreover, employing atom-structured electrodes and jellium-approximated ones for both of the Al and Si monatomic chains, we investigate how much the electron transport properties are unphysically affected by the jellium parts.

Essentially exact ground-state calculations by superpositions of nonorthogonal Slater determinants.

An essentially exact ground-state calculation algorithm for few-electron systems based on superposition of nonorthogonal Slater determinants (SDs) is described, and its convergence properties to ground states are examined. A linear combination of SDs is adopted as many-electron wave functions, and all one-electron wave functions are updated by employing linearly independent multiple correction vectors on the basis of the variational principle. The improvement of the convergence performance to the ground state given by the multi-direction search is shown through comparisons with the conventional steepest descent method. The accuracy and applicability of the proposed scheme are also demonstrated by calculations of the potential energy curves of few-electron molecular systems, compared with the conventional quantum chemistry calculation techniques.

Real-space finite-difference approach for multi-body systems: path-integral renormalization group method and direct energy minimization method.

The path-integral renormalization group and direct energy minimization method of practical first-principles electronic structure calculations for multi-body systems within the framework of the real-space finite-difference scheme are introduced. These two methods can handle higher dimensional systems with consideration of the correlation effect. Furthermore, they can be easily extended to the multicomponent quantum systems which contain more than two kinds of quantum particles. The key to the present methods is employing linear combinations of nonorthogonal Slater determinants (SDs) as multi-body wavefunctions. As one of the noticeable results, the same accuracy as the variational Monte Carlo method is achieved with a few SDs. This enables us to study the entire ground state consisting of electrons and nuclei without the need to use the Born-Oppenheimer approximation. Recent activities on methodological developments aiming towards practical calculations such as the implementation of auxiliary field for Coulombic interaction, the treatment of the kinetic operator in imaginary-time evolutions, the time-saving double-grid technique for bare-Coulomb atomic potentials and the optimization scheme for minimizing the total-energy functional are also introduced. As test examples, the total energy of the hydrogen molecule, the atomic configuration of the methylene and the electronic structures of two-dimensional quantum dots are calculated, and the accuracy, availability and possibility of the present methods are demonstrated.

Mechanism of atomic-scale passivation and flattening of semiconductor surfaces by wet-chemical preparations.

Atomic arrangements of Si(001), Si(110) and 4H-SiC(0001) surfaces after wet-chemical preparations are investigated with scanning tunneling microscopy. Their passivated structures as well as the surface formation mechanisms in aqueous solutions are discussed. On both Si(001) and Si(110) surfaces, simple 1 × 1 phases terminated by H atoms are clearly resolved after dilute HF dipping. Subsequent etching with water produces the surfaces with 'near-atomic' smoothness. The mechanisms of atomic-scale preferential etching in water are described in detail together with first-principles calculations. Furthermore, 4H-SiC(0001), which is a hard material and where it is difficult to control the surface structure by solutions, is flattened on the atomic scale with Pt as a catalyst in HF solution. After a mechanism is proposed based on electroless oxidation, the flattened surface mainly composed of a 1 × 1 phase is analyzed. The obtained results will be helpful from various scientific and technological viewpoints.

First-principles molecular-dynamics calculations on chemical reactions and atomic structures induced by H radical impinging onto Si(001)2 x 1:H surface.

Chemical reactions between hydrogen terminated Si(001)2 x 1 surface and impinging H radical are investigated by means of first-principles molecular-dynamics simulations. Reaction probabilities of abstraction of surface terminating H atom with H2 formation, adsorption onto Si surface and reflection of impinging H atom are analyzed with respect to the kinetic energy of incident H radical. The probabilities of abstraction and adsorption turn out to be ranging from 0.81 to 0.58 and from 0.19 to 0.42, respectively, while that of reflection almost zero. As initial kinetic energy of the impinging atom increases, the reaction probability of abstraction decreases and that of absorption increases. Metastable H-absorbed atomic configurations are also derived by optimizing the structures obtained in the impinging dynamics calculations. They are candidates of the so-called reservoir site which is a key to understand the unity hydrogen coverage observed after an exposure to gaseous H atom ambient despite existing residual vacant sites due to abstraction.

Electron-electron correlations in square-well quantum dots: direct energy minimization approach.

Electron-electron correlations in two-dimensional square-well quantum dots are investigated using the direct energy minimization scheme. Searches for groundstate charges and spin configurations are performed with varying the sizes of dots and the number of electrons. For a two-electron system, a standout difference between the configurations with and without counting correlation energy is demonstrated. The emergence and melting of Wigner-molecule-like structures arising from the interplay between the kinetic energy and Coulombic interaction energy are described. Electron-electron correlation energies and addition energy spectra are calculated, and special electron numbers related to peculiar effects of the square well are extracted.

Time-saving first-principles calculation method for electron transport between jellium electrodes.

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.

Total-energy minimization of few-body electron systems in the real-space finite-difference scheme.

A practical and high-accuracy computation method to search for ground states of few-electron systems is presented on the basis of the real-space finite-difference scheme. A linear combination of Slater determinants is employed as a many-electron wavefunction, and the total-energy functional is described in terms of overlap integrals of one-electron orbitals without the constraints of orthogonality and normalization. In order to execute a direct energy minimization process of the energy functional, the steepest-descent method is used. For accurate descriptions of integrals which include bare-Coulomb potentials of ions, the time-saving double-grid technique is introduced. As an example of the present method, calculations for the ground state of the hydrogen molecule are demonstrated. An adiabatic potential curve is illustrated, and the accessibility and accuracy of the present method are discussed.

First-principles study of magnetic ordering of an Al infinite single-row atomic wire.

In this paper we present a detailed analysis of the atomic and spin-electronic structure of an Al infinite single-row atomic wire (Al-ISAW). Our work is based on ab initio self-consistent field calculations within the local density approximation, and we predict structural transformations during elongation using the norm-conserving (NC) and projector augmented-wave (PAW) pseudopotentials. The results obtained by the NC pseudopotential are in good agreement with those obtained by the PAW pseudopotential. We confirm that the Al-ISAW shows a metal-insulator transition and fractures when elongated beyond the equilibrium length. Then, a wire with antiferromagnetic ordering is found to be the lowest energetically. We find that the magnitude of spin polarization in the vicinity of nuclei is marginal and does not play an important role in the Peierls instability. The present results show that the NC pseudopotential can give an accurate physical picture of the atomic and spin-electronic structures of the Al-ISAW.

First-principles study of electron-conduction properties of C60 bridges.

The electron-conduction properties of fullerene-based nanostructures suspended between electrodes are examined by first-principles calculations based on the density functional theory. The electron conductivity of the C60-dimer bridge is low owing to the constraint of the junction of the molecules. When the fullerenes are doped electrons by being inserted Li atoms into the cages, the unoccupied state around the junction is filled and the conductivity can be significantly improved.

Relationship between the geometric structure and conductance oscillation in nanowires.

A theoretical analysis of the electron transport properties of plain and bumpy jellium nanowires suspended between semi-infinite jellium electrodes is carried out, and the possibility of the experimental observation of the conductance oscillation with a period longer than the two-atom length is discussed. In both the nanowires, the transmission trace as a function of the nanowire length exhibits oscillatory behaviour. The period of the oscillation of the plain nanowire corresponds to π divided by the Bloch wavenumber of the electrons in the nanowire region. However, the period of the oscillation of the bumpy nanowire results in the least common multiple of π divided by the Bloch wavenumber and the geometric period of the nanowire. Our result indicates that the conductance oscillation with a period longer than the two-atom length can be experimentally observed if nanowires without any defects are formed in experiments.

First-principles study of the electronic structures and dielectric properties of the Si/SiO(2) interface.

A first-principles study of the electronic structures and dielectric properties of Si/SiO(2) interfaces is implemented. Comparing the interfaces with and without defects, we explore the relationship between the defects and the dielectric properties, and also discuss the effect of the defects on the leakage current between the gate electrode and silicon substrate. We found that the electrons around the Fermi level percolate into the SiO(2) layers, which reduces the effective oxide thickness and is expected to enhance the leakage current. The dangling bonds largely affect the dielectric properties of the interface and the termination of dangling bonds by hydrogen atoms is successful in suppressing the increase of the dielectric constant.

A path-integration calculation method based on the real-space finite-difference scheme.

We propose a new path-integration calculation method to treat the time evolution of a wavefunction within the framework of the real-space finite-difference formalism, and also develop an effective scheme to compute the scattering wavefunction for an incident electron with arbitrary energy, in which an impulse wavefunction is adopted as an initial state of the time evolution. In this method, once the time evolution of the initial impulse wavefunction is calculated, all of the solutions in the scattering problem can be derived by means of Fourier analysis of the time-evolved wavefunction, which leads to a reduction of the calculation time. In order to test the applicability of our newly developed simulation procedures, we implemented simulations for the one-dimensional scattering problem. Each simulation showed the usefulness of the present scheme by yielding the steady scattering states in agreement with exact ones.

Order-N first-principles calculation method for self-consistent ground-state electronic structures of semi-infinite systems.

We present an efficient and highly accurate first-principles calculation method with linear system-size scaling to determine the self-consistent ground-state electron-charge densities of nanostructures suspended between semi-infinite bulks by directly minimizing the energy functional. By making efficient use of the advantages of the real-space finite-difference method, we can impose arbitrary boundary conditions on models and employ spatially localized orbitals. These advantages enable us to calculate the ground-state electron-charge densities in semi-infinite systems. Examples of electronic structure calculations for a one-dimensional case and a conductance calculation for sodium nanowires are presented. The calculated electronic structure of the one-dimensional system agrees well with the exact analytical solution, and the conduction properties of the sodium nanowires are consistent with experimental and other theoretical results. These results imply that our procedure enables us to accurately compute self-consistent electronic structures of semi-infinite systems.

First-principles study of electron-conduction properties of helical gold nanowires.

Multishell helical gold nanowires (HGNs) suspended between semi-infinite electrodes are found to exhibit peculiar electron-conduction properties by first-principles calculations based on the density functional theory. Our results that the numbers of conduction channels in the HGNs and their conductances are smaller than those expected from a single-atom row nanowire verify the recent experiment. In addition, we obtained a more striking result that, in the cases of thin HGNs, distinct magnetic fields are induced by the electronic current helically flowing around the shells. This finding indicates that the HGNs can be good candidates for nanometer-scale solenoids.