Ebook: Electron Scattering in Solid Matter: A Theoretical and Computational Treatise

Addressing graduate students and researchers, this book gives a very detailed theoretical and computational description of multiple scattering in solid matter. Particular emphasis is placed on solids with reduced dimensions, on full potential approaches and on relativistic treatments. For the first time approaches such as the Screened Korringa-Kohn-Rostoker method that have emerged during the last 5 – 10 years are reviewed, considering all formal steps such as single-site scattering, structure constants and screening transformations, and also the numerical point of view. Furthermore, a very general approach is presented for solving the Poisson equation, needed within density functional theory in order to achieve self-consistency. Going beyond ordered matter and translationally invariant systems, special chapters are devoted to the Coherent Potential Approximation and to the Embedded Cluster Method, used, for example, for describing nanostructured matter in real space. In a final chapter, physical properties related to the (single-particle) Green’s function, such as magnetic anisotropies, interlayer exchange coupling, electric and magneto-optical transport and spin-waves, serve to illustrate the usefulness of the methods described.

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Addressing graduate students and researchers, this book gives a very detailed theoretical and computational description of multiple scattering in solid matter. Particular emphasis is placed on solids with reduced dimensions, on full potential approaches and on relativistic treatments. For the first time approaches such as the Screened Korringa-Kohn-Rostoker method that have emerged during the last 5 – 10 years are reviewed, considering all formal steps such as single-site scattering, structure constants and screening transformations, and also the numerical point of view. Furthermore, a very general approach is presented for solving the Poisson equation, needed within density functional theory in order to achieve self-consistency. Going beyond ordered matter and translationally invariant systems, special chapters are devoted to the Coherent Potential Approximation and to the Embedded Cluster Method, used, for example, for describing nanostructured matter in real space. In a final chapter, physical properties related to the (single-particle) Green’s function, such as magnetic anisotropies, interlayer exchange coupling, electric and magneto-optical transport and spin-waves, serve to illustrate the usefulness of the methods described.

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Addressing graduate students and researchers, this book gives a very detailed theoretical and computational description of multiple scattering in solid matter. Particular emphasis is placed on solids with reduced dimensions, on full potential approaches and on relativistic treatments. For the first time approaches such as the Screened Korringa-Kohn-Rostoker method that have emerged during the last 5 – 10 years are reviewed, considering all formal steps such as single-site scattering, structure constants and screening transformations, and also the numerical point of view. Furthermore, a very general approach is presented for solving the Poisson equation, needed within density functional theory in order to achieve self-consistency. Going beyond ordered matter and translationally invariant systems, special chapters are devoted to the Coherent Potential Approximation and to the Embedded Cluster Method, used, for example, for describing nanostructured matter in real space. In a final chapter, physical properties related to the (single-particle) Green’s function, such as magnetic anisotropies, interlayer exchange coupling, electric and magneto-optical transport and spin-waves, serve to illustrate the usefulness of the methods described.

Content:
Front Matter....Pages I-XV
Introduction....Pages 1-4
Preliminary definitions....Pages 5-9
Multiple scattering....Pages 11-44
Shape functions....Pages 45-56
Non-relativistic single-site scattering for spherically symmetric potentials....Pages 57-64
Non-relativistic full potential single-site scattering....Pages 65-79
Spin-polarized non-relativistic single-site scattering....Pages 81-82
Relativistic single-site scattering for spherically symmetric potentials....Pages 83-90
Relativistic full potential single-site scattering....Pages 91-94
Spin-polarized relativistic single-site scattering for spherically symmetric potentials....Pages 95-107
Spin-polarized relativistic full potential single-site scattering....Pages 109-128
Scalar-relativistic single-site scattering for spherically symmetric potentials....Pages 129-133
Scalar-relativistic full potential single-site scattering....Pages 135-138
Phase shifts and resonance energies....Pages 139-144
Structure constants....Pages 145-160
Green’s functions: an in-between summary....Pages 161-162
The Screened KKR method for two-dimensional translationally invariant systems....Pages 163-176
Charge and magnetization densities....Pages 177-201
The Poisson equation and the generalized Madelung problem for two- and three-dimensional translationally invariant systems....Pages 203-233
“Near field” corrections....Pages 235-245
Practical aspects of full-potential calculations....Pages 247-252
Total energies....Pages 253-274
The Coherent Potential Approximation....Pages 275-291
The embedded cluster method....Pages 293-298
Magnetic configurations — rotations of frame....Pages 299-309
Related physical properties....Pages 311-373
Back Matter....Pages 375-382

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Addressing graduate students and researchers, this book gives a very detailed theoretical and computational description of multiple scattering in solid matter. Particular emphasis is placed on solids with reduced dimensions, on full potential approaches and on relativistic treatments. For the first time approaches such as the Screened Korringa-Kohn-Rostoker method that have emerged during the last 5 – 10 years are reviewed, considering all formal steps such as single-site scattering, structure constants and screening transformations, and also the numerical point of view. Furthermore, a very general approach is presented for solving the Poisson equation, needed within density functional theory in order to achieve self-consistency. Going beyond ordered matter and translationally invariant systems, special chapters are devoted to the Coherent Potential Approximation and to the Embedded Cluster Method, used, for example, for describing nanostructured matter in real space. In a final chapter, physical properties related to the (single-particle) Green’s function, such as magnetic anisotropies, interlayer exchange coupling, electric and magneto-optical transport and spin-waves, serve to illustrate the usefulness of the methods described.

Content:
Front Matter....Pages I-XV
Introduction....Pages 1-4
Preliminary definitions....Pages 5-9
Multiple scattering....Pages 11-44
Shape functions....Pages 45-56
Non-relativistic single-site scattering for spherically symmetric potentials....Pages 57-64
Non-relativistic full potential single-site scattering....Pages 65-79
Spin-polarized non-relativistic single-site scattering....Pages 81-82
Relativistic single-site scattering for spherically symmetric potentials....Pages 83-90
Relativistic full potential single-site scattering....Pages 91-94
Spin-polarized relativistic single-site scattering for spherically symmetric potentials....Pages 95-107
Spin-polarized relativistic full potential single-site scattering....Pages 109-128
Scalar-relativistic single-site scattering for spherically symmetric potentials....Pages 129-133
Scalar-relativistic full potential single-site scattering....Pages 135-138
Phase shifts and resonance energies....Pages 139-144
Structure constants....Pages 145-160
Green’s functions: an in-between summary....Pages 161-162
The Screened KKR method for two-dimensional translationally invariant systems....Pages 163-176
Charge and magnetization densities....Pages 177-201
The Poisson equation and the generalized Madelung problem for two- and three-dimensional translationally invariant systems....Pages 203-233
“Near field” corrections....Pages 235-245
Practical aspects of full-potential calculations....Pages 247-252
Total energies....Pages 253-274
The Coherent Potential Approximation....Pages 275-291
The embedded cluster method....Pages 293-298
Magnetic configurations — rotations of frame....Pages 299-309
Related physical properties....Pages 311-373
Back Matter....Pages 375-382
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