First-principles calculation method for electron transport based on 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 metal electrodes. The results confirm that the leakage current through the (001)Si/SiO$_2$ model becomes much larger when the dangling-bond (DB) state is induced by a defect in the oxygen layer while that through the (001)Ge/GeO$_2$ model is insensitive to the DB state

Magnetic orderings in Al nanowires suspended between electrodes

A theoretical analysis of a relation between atomic and spin-electronic structures for the ground state of single-row aluminum nanowires suspended between Al(001) electrodes is demonstrated using first-principles molecular-dynamics simulations. We obtain a unusual result that a 3-aluminum-atom nanowire sandwiched between the electrodes does not manifest magnetic ordering although an isolated aluminum trimer molecule in a straight line is spin-polarized. On the other hand, a 5-atom nanowire exhibits ferromagnetic ordering, where three central atoms form a spin-polarized trimer. Moreover, in the case of an 8-atom nanowire, the middle atoms in the nanowire form two spin-polarized trimers with antiferromagnetic ordering.Comment: 9 page

Improvement of accuracy of wave-function-matching method for transport calculation

The wave-function-matching (WFM) technique for first-principles transport-property calculations was modified by S\o{}rensen {\it et al.} so as to exclude rapidly decreasing evanescent waves [S\o{}rensen {\it et al.}, Phys. Rev. B {\bf 77}, 155301 (2008)]. However, this method lacks translational invariance of the transmission probability with respect to insertion of matching planes and consistency between the sum of the transmission and reflection probabilities and the number of channels in the transition region. We reformulate the WFM method since the original methods are formulated to include all the generalized Bloch waves. It is found that the translational invariance is destroyed by the overlap of the layers between the electrode and transition regions and by the pseudoinverses used to exclude the rapidly decreasing evanescent waves. We then devise a method that removes the overlap and calculates the transmission probability without the pseudoinverses. As a result, we find that the translational invariance of the transmission probability with respect to insertion of the extra layers is properly retained and the sum of the transmission and reflection probabilities exactly agrees with the number of channels. In addition, we prove that the accuracy in the transmission probability of this WFM technique is comparable with that obtained by the nonequilibrium Green's function method. Furthermore, we carry out the electron transport calculations on two-dimensional graphene sheets embedded with B--N line defects sandwiched between a pair of semi-infinite graphene electrodes and find the dependence of the electron transmission on the transverse momentum perpendicular to the direction of transport

Sudden Suppression of Electron-Transmission Peaks in Finite-Biased Nanowires

Negative differential conductance (NDC) is expected to be an essential property to realize fast switching in future electronic devices. We here present a thorough analysis on electron transportability of a simple atomic-scale model consisting of square prisms, and clarify the detailed mechanism of the occurrence of NDC phenomenon in terms of the changes of local density of states upon applying bias voltages to the electrodes. Boosting up bias voltages, we observe sudden suppression of transmission peaks which results in NDC behavior in the current-voltage characteristic. This suppression is explained by the fact that when the bias voltage exceeds a certain threshold, the conduction channels contributing to the current flow are suddenly closed up to deny the electron transportation.Comment: 12 text pages, 6 figure

Contour integral method for obtaining the self-energy matrices of electrodes in electron transport calculations

We propose an efficient computational method for evaluating the self-energy matrices of electrodes to study ballistic electron transport properties in nanoscale systems. To reduce the high computational cost incurred in large systems, a contour integral eigensolver based on the Sakurai-Sugiura method combined with the shifted biconjugate gradient method is developed to solve exponential-type eigenvalue problem for complex wave vectors. A remarkable feature of the proposed algorithm is that the numerical procedure is very similar to that of conventional band structure calculations. We implement the developed method in the framework of the real-space higher-order finite difference scheme with nonlocal pseudopotentials. Numerical tests for a wide variety of materials validate the robustness, accuracy, and efficiency of the proposed method. As an illustration of the method, we present the electron transport property of the free-standing silicene with the line defect originating from the reversed buckled phases.Comment: 36 pages, 13 figures, 2 table

Efficient calculation of the Green's function in scattering region for electron-transport simulations

We propose a first-principles method of efficiently evaluating electron-transport properties of very long systems. Implementing the recursive Green's function method and the shifted conjugate gradient method in the transport simulator based on real-space finite-difference formalism, we can suppress the increase in the computational cost, which is generally proportional to the cube of the system length to a linear order. This enables us to perform the transport calculations of double-walled carbon nanotubes~(DWCNTs) with 196,608 atoms. We find that the conductance spectra exhibit different properties depending on the periodicity of doped impurities in DWCNTs and they differ from the properties for systems with less than 1,000 atoms.Comment: 13 pages, 5 figures, 1 tabl

Real-space electronic-structure calculations with full-potential all-electron precision for transition-metals

We have developed an efficient computational scheme utilizing the real-space finite-difference formalism and the projector augmented-wave (PAW) method to perform precise first-principles electronic-structure simulations based on the density functional theory for systems containing transition metals with a modest computational effort. By combining the advantages of the time-saving double-grid technique and the Fourier filtering procedure for the projectors of pseudopotentials, we can overcome the egg box effect in the computations even for first-row elements and transition metals, which is a problem of the real-space finite-difference formalism. In order to demonstrate the potential power in terms of precision and applicability of the present scheme, we have carried out simulations to examine several bulk properties and structural energy differences between different bulk phases of transition metals, and have obtained excellent agreement with the results of other precise first-principles methods such as a plane wave based PAW method and an all-electron full-potential linearized augmented plane wave (FLAPW) method.Comment: 29 Page

Real-space method for first-principles electron transport calculations: Self-energy terms of electrodes for large systems

We present a fast and stable numerical technique to obtain the self-energy terms of electrodes for first-principles electron transport calculations. Although first-principles calculations based on the real-space finite-difference method are advantageous for execution on massively parallel computers, large-scale transport calculations are hampered by the computational cost and numerical instability of the computation of the self-energy terms. Using the orthogonal complement vectors of the space spanned by the generalized Bloch waves that actually contribute to transport phenomena, the computational accuracy of transport properties is significantly improved with a moderate computational cost. To demonstrate the efficiency of the present technique, the electron transport properties of a Stone-Wales (SW) defect in graphene and silicene are examined. The resonance scattering of the SW defect is observed in the conductance spectrum of silicene since the σ∗ state of silicene lies near the Fermi energy. In addition, we found that one conduction channel is sensitive to a defect near the Fermi energy, while the other channel is hardly affected. This characteristic behavior of the conduction channels is interpreted in terms of the bonding network between the bilattices of the honeycomb structure in the formation of the SW defect. The present technique enables us to distinguish the different behaviors of the two conduction channels in graphene and silicene owing to its excellent accuracy