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作者 Hirose, Kikuji
書名 First-principles Calculations In Real-space Formalism : Electronic Configurations and Transport Properties of Nanostructures
出版項 Singapore : World Scientific Publishing Company, 2005
國際標準書號 9781860946530 (electronic bk.)
book jacket
說明 1 online resource (265 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
附註 Intro -- Preface -- Contents -- PART I Real-Space Finite-Difference Method for First-Principles Calculations -- Chapter 1 Foundations of Methodology -- 1.1 Real-Space Finite-Difference Method -- 1.2 Density-Functional Theory and Kohn-Sham Equation -- 1.3 Finite-Difference Formulas -- 1.4 Real-Space Representation of Kohn-Sham Equation -- 1.5 Norm-Conserving Pseudopotentials -- 1.6 Hellmann-Feynman Forces Acting on Atoms -- Chapter 2 Solvers of the Poisson Equation and Related Techniques -- 2.1 The Real-Space Representation of the Poisson Equation -- 2.2 The Fuzzy Cell Decomposition and Multipole Expansion Technique -- 2.3 Algorithm to Generate the Fuzzy Cell -- 2.4 Illustration for Efficiency of the Fuzzy Cell Decomposition and Multipole Expansion Method -- 2.5 Conjugate-Gradient Method -- 2.6 Conjugate-Gradient Acceleration -- 2.7 Multigrid Method -- Chapter 3 Minimization Procedures of the Energy Functional -- 3.1 Introduction -- 3.2 Approach of Minimizing the Kohn-Sham Energy Functional -- 3.3 Approach of Minimizing the Kohn-Sham Eigenvalues -- 3.4 Multigrid Method for Minimizing the Kohn-Sham Energy Functional -- 3.5 Fermi-Broadening Technique -- 3.6 Approach of Directly Minimizing the Energy Functional -- 3.7 Illustration for Direct Minimization Efficiency -- 3.8 Application of the Direct Minimization: Order-N Calculations for Gold Nanowires -- Chapter 4 Timesaving Double-Grid Technique -- 4.1 Essential Feature of the Timesaving Double-Grid Technique -- 4.2 Illustration of Double-Grid Efficiency -- 4.3 Other Mesh-Refinement Techniques -- Chapter 5 Implementation for Systems under Various Boundary Conditions -- 5.1 Isolated Boundary Condition: Molecules -- 5.2 3D Periodic Boundary Condition: Crystals -- 5.3 (2D Periodic + 1D Isolated) Boundary Condition: Thin Films -- 5.4 (1D Periodic + 2D Isolated) Boundary Condition: Infinite Metallic Wires
5.5 Twist Boundary Condition: Infinite Helical Carbon Nanotubes -- PART II Electronic Transport through Nanostructures between Semi-Infinite Electrodes -- Chapter 6 Basic Scheme of the Overbridging Boundary-Matching Method -- 6.1 Preliminary Concepts: Ballistic Transport of Electrons and the Landauer Formula -- 6.2 Wave-Function Matching Procedure -- 6.3 Computational Scheme for Generalized Bloch States I. The Generalized Eigenvalue Equation -- 6.4 Computational Scheme for Generalized Bloch States II. The Continued-Fraction Equations -- 6.5 Related Considerations -- 6.6 Application: Sodium Nanowires -- Chapter 7 Inclusion of Norm-Conserving Pseudopotentials -- 7.1 Treatment of Nonlocal Pseudopotentials -- 7.2 Application: Aluminum Nanowire -- Chapter 8 Jellium Electrode Approximation -- 8.1 Generalized Bloch States in Jellium Electrodes -- 8.2 Application: Helical Gold Nanowires -- 8.3 Application: Fullerene Chains -- Chapter 9 Green's Function Formalism and the Overbridging Boundary-Matching Scheme -- 9.1 Preliminary Remarks -- 9.2 Green's Functions in the Discretized Space within the Real-Space Finite-Difference Framework -- 9.3 Green's Function of a Whole System Including the Transition Region and Two Semi-Infinite Electrodes -- 9.4 Green's Function Matching in the Overbridging Boundary-Matching Scheme and Related Topics -- 9.5 Green's Function of a Whole System with a Block-Tridiagonal Hamiltonian Matrix -- Chapter 10 Calculation Method Based on the Lippmann-Schwinger Equation -- 10.1 The Lippmann-Schwinger Equation -- 10.2 Correction of Effective Potentials inside Electrodes at a Finite Bias Voltage -- 10.3 Application: Sodium Nanowire under Finite Bias Voltages -- Appendix A Formulas for Long-Range Potentials under Various Boundary Conditions -- A.1 3D Periodic Boundary Condition -- Ionic pseudopotential -- Hartree potential
Coulomb energy among the nuclei -- A.2 (2D Periodic + 1D Isolated) Boundary Condition -- Ionic pseudopotential -- Hartree potential -- Coulomb energy among the nuclei -- A.3 (1D Periodic + 2D Isolated) Boundary Condition -- Ionic pseudopotential -- Hartree potential -- Coulomb energy among the nuclei -- A.4 Twist Boundary Condition -- A.5 Uneven 2D Periodic Boundary Condition -- A.6 Uneven 3D Periodic Boundary Condition -- Appendix B Tight-Binding Approach Based on the Overbridging Boundary-Matching Scheme -- B.1 Generalized Bloch States inside Semi-Infinite Crystalline Electrodes -- B.2 Wave-Function Matching Procedure -- B.3 Green's Function Formalism -- Bibliography -- Index
With cutting-edge materials and minute electronic devices being produced by the latest nanoscale fabrication technology, it is essential for scientists and engineers to rely on first-principles (ab initio) calculation methods to fully understand the electronic configurations and transport properties of nanostructures. It is now imperative to introduce practical and tractable calculation methods that accurately describe the physics in nanostructures suspended between electrodes.This timely volume addresses novel methods for calculating electronic transport properties using real-space formalisms free from geometrical restrictions. The book comprises two parts: The first details the basic formalism of the real-space finite-difference method and its applications. This provides the theoretical foundation for the second part of the book, which presents the methods for calculating the properties of electronic transport through nanostructures sandwiched by semi-infinite electrodes
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Hirose, Kikuji First-principles Calculations In Real-space Formalism: Electronic Configurations And Transport Properties Of Nanostructures Singapore : World Scientific Publishing Company,c2005 9781860945120
主題 Nanostructures.;Nanotechnology
Electronic books
Alt Author Ono, Tomoya
Fujimoto, Yoshitaka
Tsukamoto, Shigeru
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