Krylov subspace method for evaluating the self-energy matrices in electron transport calculations

Hans Henrik Brandenborg Sørensen, Per Christian Hansen, D. E. Petersen, S. Skelboe, Kurt Stokbro

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    Abstract

    We present a Krylov subspace method for evaluating the self-energy matrices used in the Green's function formulation of electron transport in nanoscale devices. A procedure based on the Arnoldi method is employed to obtain solutions of the quadratic eigenvalue problem associated with the infinite layered systems of the electrodes. One complex and two real shift-and-invert transformations are adopted to select interior eigenpairs with complex eigenvalues on or in the vicinity of the unit circle that correspond to the propagating and evanescent modes of most influence in electron transport calculations. Numerical tests within a density functional theory framework are provided to validate the accuracy and robustness of the proposed method, which in most cases is an order of magnitude faster than conventional methods.
    Original languageEnglish
    JournalPhysical Review B Condensed Matter
    Volume77
    Issue number15
    Pages (from-to)155301
    ISSN0163-1829
    DOIs
    Publication statusPublished - 2008

    Bibliographical note

    Copyright 2008 American Physical Society

    Keywords

    • CONDUCTANCE
    • GREENS-FUNCTION
    • FORMULA
    • ARNOLDI ALGORITHM
    • COMPLEX SHIFT
    • SURFACES
    • JUNCTIONS
    • QUADRATIC EIGENVALUE PROBLEM

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