A hierarchical research by large-scale and ab initio electronic structure theories -- Si and Ge cleavage and stepped (111)-2x1 surfaces --

The ab initio calculation with the density functional theory and plane-wave bases is carried out for stepped Si(111)-2x1 surfaces that were predicted in a cleavage simulation by the large-scale (order-N) electronic structure theory (T. Hoshi, Y. Iguchi and T. Fujiwara, Phys. Rev. B72 (2005) 075323). The present ab initio calculation confirms the predicted stepped structure and its bias-dependent STM image. Moreover, two (meta)stable step-edge structures are found and compared. The investigation is carried out also for Ge(111)-2x1 surfaces, so as to construct a common understanding among elements. The present study demonstrates the general importance of the hierarchical research between large-scale and ab initio electronic structure theories.Comment: 5 pages, 4 figures, to appear in Physica

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

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

Visualization of Radiation Distribution with High Sensitive CCD Camera

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