Million-atom molecular dynamics simulation by order-N electronic structure theory and parallel computation

Parallelism of tight-binding molecular dynamics simulations is presented by means of the order-N electronic structure theory with the Wannier states, recently developed (J. Phys. Soc. Jpn. 69,3773 (2000)). An application is tested for silicon nanocrystals of more than millions atoms with the transferable tight-binding Hamiltonian. The efficiency of parallelism is perfect, 98.8 %, and the method is the most suitable to parallel computation. The elapse time for a system of $2\times 10^6$ atoms is 3.0 minutes by a computer system of 64 processors of SGI Origin 3800. The calculated results are in good agreement with the results of the exact diagonalization, with an error of 2 % for the lattice constant and errors less than 10 % for elastic constants.Comment: 5 pages, 3 figure

An order-N electronic structure theory with generalized eigenvalue equations and its application to a ten-million-atom system

A linear-algebraic theory called 'multiple Arnoldi method' is presented and realizes large-scale (order-N) electronic structure calculation with generalized eigen-value equations. A set of linear equations, in the form of (zS-H) x = b, are solved simultaneously with multiple Krylov subspaces. The method is implemented in a simulation package ELSES (http://www.elses.jp) with tight-binding-form Hamiltonians. A finite-temperature molecular dynamics simulation is carried out for metallic and insulating materials. A calculation with $10^7$ atoms was realized by a workstation. The parallel efficiency is shown upto 1,024 CPU cores.Comment: 9 pages, 3 figures. To appear in J. Phys.: Condens. Matte

Very early responses to colour stimuli detected in prestriate visual cortex by magnetoencephalography (MEG)

Our previous studies with the visual motion and form systems show that visual stimuli belonging to these categories trigger much earlier latency responses from the visual cortex than previously supposed and that the source of the earliest signals can be located in either the prestriate cortex or in both the striate (V1) and prestriate cortex. This is consistent with the known anatomical connections since, in addition to the classical retino-geniculo-striate cortex input to the prestriate visual areas, there are direct anatomical inputs from both the lateral geniculate nucleus and the pulvinar that reach the prestriate visual cortex without passing through striate cortex. In pursuing our studies, we thought it especially interesting to study another cardinal visual attribute, namely colour, to learn whether colour stimuli also provoke very early responses, at less than 50 ms from visual cortex. To address the question, we asked participants to view stimuli that changed in colour and used magneto-encephalography to detect very early responses (< 50 ms) in the occipital visual cortex. Our results show that coloured stimuli also provoke an early cortical response (M30), with an average peak time at 31.7 ms, thus bringing the colour system into line with the visual motion and form systems. We conclude that colour signals reach visual cortex, including prestriate visual cortex, earlier than previously supposed

Krylov Subspace Method for Molecular Dynamics Simulation based on Large-Scale Electronic Structure Theory

For large scale electronic structure calculation, the Krylov subspace method is introduced to calculate the one-body density matrix instead of the eigenstates of given Hamiltonian. This method provides an efficient way to extract the essential character of the Hamiltonian within a limited number of basis set. Its validation is confirmed by the convergence property of the density matrix within the subspace. The following quantities are calculated; energy, force, density of states, and energy spectrum. Molecular dynamics simulation of Si(001) surface reconstruction is examined as an example, and the results reproduce the mechanism of asymmetric surface dimer.Comment: 7 pages, 3 figures; corrected typos; to be published in Journal of the Phys. Soc. of Japa

Spin accumulation created electrically in an n-type germanium channel using Schottky tunnel contacts

Using high-quality Fe$_{3}$Si/$n^{+}$-Ge Schottky-tunnel-barrier contacts, we study spin accumulation in an $n$-type germanium ($n$-Ge) channel. In the three- or two-terminal voltage measurements with low bias current conditions at 50 K, Hanle-effect signals are clearly detected only at a forward-biased contact. These are reliable evidence for electrical detection of the spin accumulation created in the $n$-Ge channel. The estimated spin lifetime in $n$-Ge at 50 K is one order of magnitude shorter than those in $n$-Si reported recently. The magnitude of the spin signals cannot be explained by the commonly used spin diffusion model. We discuss a possible origin of the difference between experimental data and theoretical values.Comment: 4 pages, 3 figures, To appear in J. Appl. Phy

Dynamical brittle fractures of nanocrystalline silicon using large-scale electronic structure calculations

A hybrid scheme between large-scale electronic structure calculations is developed and applied to nanocrystalline silicon with more than 10$^5$ atoms. Dynamical fracture processes are simulated under external loads in the [001] direction. We shows that the fracture propagates anisotropically on the (001) plane and reconstructed surfaces appear with asymmetric dimers. Step structures are formed in larger systems, which is understood as the beginning of a crossover between nanoscale and macroscale samples.Comment: 10 pages, 4 figure

Linear Algebraic Calculation of Green's function for Large-Scale Electronic Structure Theory

A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the density matrix without calculating eigenstates.The problem is reduced to independent linear equations at many energy points and the calculation is actually carried out only for a single energy point. The method is robust against the round-off error and the calculation can reach the machine accuracy. With the observation of residual vectors, the accuracy can be controlled, microscopically, independently for each element of the Green's function, and dynamically, at each step in dynamical simulations. The method is applied to both semiconductor and metal.Comment: 10 pages, 9 figures. To appear in Phys. Rev. B. A PDF file with better graphics is available at http://fujimac.t.u-tokyo.ac.jp/lses