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E-raamat: Electronic Structure: Basic Theory and Practical Methods

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  • Ilmumisaeg: 27-Aug-2020
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108596763
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Electronic Structure: Basic Theory and Practical MethodsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 27-Aug-2020
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108596763
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The study of electronic structure of materials is at a momentous stage, with new computational methods and advances in basic theory. Many properties of materials can be determined from the fundamental equations, and electronic structure theory is now an integral part of research in physics, chemistry, materials science and other fields. This book provides a unified exposition of the theory and methods, with emphasis on understanding each essential component. New in the second edition are recent advances in density functional theory, an introduction to Berry phases and topological insulators explained in terms of elementary band theory, and many new examples of applications. Graduate students and research scientists will find careful explanations with references to original papers, pertinent reviews, and accessible books. Each chapter includes a short list of the most relevant works and exercises that reveal salient points and challenge the reader.

Electronic structure is the most highly referenced field in physics, making possible calculation of materials from the fundamental equations of quantum mechanics. This book is written for graduate students and research scientists in physics, chemistry and materials science, explaining the basic theory and the most-used computational methods.

Arvustused

' this 2nd edition is very welcome and timely, as it has been significantly expanded to cover the 'new' topics. The core of the book remains unchanged in scope, focusing on 'independent particle methods' such as DFT and Hartree-Fock theory, and their extensions. This is a worthy and is strongly recommended for anyone working in the field of electronic structure.' Matt Probert, Contemporary Physics

Muu info

An authoritative text in condensed matter physics, unifying theory and methods to present electronic structure to students and researchers.
Preface xix
Acknowledgments xxiv
List of Notation
xxvi
Part I Overview and Background Topics
1 Introduction
1(14)
1.1 Quantum Theory and the Origins of Electronic Structure
2(1)
1.2 Why Is the Independent-Electron Picture So Successful?
3(4)
1.3 Emergence of Quantitative Calculations
7(3)
1.4 The Greatest Challenge: Electron Interaction and Correlation
10(1)
1.5 Density Functional Theory
11(1)
1.6 Electronic Structure Is Now an Essential Part of Research
11(1)
1.7 Materials by Design
12(1)
1.8 Topology of Electronic Structure
13(2)
2 Overview
15(45)
2.1 Electronic Structure and the Properties of Matter
15(2)
2.2 Electronic Ground State: Bonding and Characteristic Structures
17(2)
2.3 Volume or Pressure As the Most Fundamental Variable
19(2)
2.4 How Good Is DFT for Calculation of Structures?
21(2)
2.5 Phase Transitions under Pressure
23(3)
2.6 Structure Prediction: Nitrogen Solids and Hydrogen Sulfide Superconductors at High Pressure
26(5)
2.7 Magnetism and Electron-Electron Interactions
31(2)
2.8 Elasticity: Stress-Strain Relations
33(2)
2.9 Phonons and Displacive Phase Transitions
35(3)
2.10 Thermal Properties: Solids, Liquids, and Phase Diagrams
38(6)
2.11 Surfaces and Interfaces
44(3)
2.12 Low-Dimensional Materials and van der Waals Heterostructures
47(1)
2.13 Nanomaterials: Between Molecules and Condensed Matter
48(2)
2.14 Electronic Excitations: Bands and Bandgaps
50(4)
2.15 Electronic Excitations and Optical Spectra
54(3)
2.16 Topological Insulators
57(1)
2.17 The Continuing Challenge: Electron Correlation
57(3)
3 Theoretical Background
60(21)
3.1 Basic Equations for Interacting Electrons and Nuclei
60(4)
3.2 Coulomb Interaction in Condensed Matter
64(1)
3.3 Force and Stress Theorems
65(2)
3.4 Generalized Force Theorem and Coupling Constant Integration
67(1)
3.5 Statistical Mechanics and the Density Matrix
68(1)
3.6 Independent-Electron Approximations
69(5)
3.7 Exchange and Correlation
74(7)
Exercises
78(3)
4 Periodic Solids and Electron Bands
81(28)
4.1 Structures of Crystals: Lattice + Basis
81(9)
4.2 Reciprocal Lattice and Brillouin Zone
90(4)
4.3 Excitations and the Bloch Theorem
94(4)
4.4 Time-Reversal and Inversion Symmetries
98(2)
4.5 Point Symmetries
100(1)
4.6 Integration over the Brillouin Zone and Special Points
101(4)
4.7 Density of States
105(4)
Exercises
106(3)
5 Uniform Electron Gas and sp-Bonded Metals
109(20)
5.1 The Electron Gas
109(2)
5.2 Noninteracting and Hartree-Fock Approximations
111(6)
5.3 Correlation Hole and Energy
117(4)
5.4 Binding in sp-Bonded Metals
121(1)
5.5 Excitations and the Lindhard Dielectric Function
122(7)
Exercises
126(3)
Part II Density Functional Theory
6 Density Functional Theory: Foundations
129(16)
6.1 Overview
129(1)
6.2 Thomas-Fermi-Dirac Approximation
130(1)
6.3 The Hohenberg-Kohn Theorems
131(4)
6.4 Constrained Search Formulation of DFT
135(2)
6.5 Extensions of Hohenberg-Kohn Theorems
137(2)
6.6 Intricacies of Exact Density Functional Theory
139(2)
6.7 Difficulties in Proceeding from the Density
141(4)
Exercises
143(2)
7 The Kohn-Sham Auxiliary System
145(26)
7.1 Replacing One Problem with Another
145(3)
7.2 The Kohn-Sham Variational Equations
148(2)
7.3 Solution of the Self-Consistent Coupled Kohn-Sham Equations
150(7)
7.4 Achieving Self-Consistency
157(3)
7.5 Force and Stress
160(1)
7.6 Interpretation of the Exchange-Correlation Potential Vxc
161(1)
7.7 Meaning of the Eigenvalues
162(1)
7.8 Intricacies of Exact Kohn-Sham Theory
163(3)
7.9 Time-Dependent Density Functional Theory
166(1)
7.10 Other Generalizations of the Kohn-Sham Approach
167(4)
Exercises
168(3)
8 Functionals for Exchange and Correlation I
171(17)
8.1 Overview
171(1)
8.2 Exc and the Exchange-Correlation Hole
172(2)
8.3 Local (Spin) Density Approximation (LSDA)
174(1)
8.4 How Can the Local Approximation Possibly Work As Well As It Does?
175(4)
8.5 Generalized-Gradient Approximations (GGAs)
179(4)
8.6 LDA and GGA Expressions for the Potential V Jc(r)
183(2)
8.7 Average and Weighted Density Formulations: ADA and WDA
185(1)
8.8 Functionals Fitted to Databases
185(3)
Exercises
186(2)
9 Functionals for Exchange and Correlation II
188(27)
9.1 Beyond the Local Density and Generalized Gradient Approximations
188(1)
9.2 Generalized Kohn-Sham and Bandgaps
189(2)
9.3 Hybrid Functionals and Range Separation
191(4)
9.4 Functionals of the Kinetic Energy Density: Meta-GGAs
195(2)
9.5 Optimized Effective Potential
197(2)
9.6 Localized-Orbital Approaches: SIC and DFT+U
199(4)
9.7 Functionals Derived from Response Functions
203(2)
9.8 Nonlocal Functionals for van der Waals Dispersion Interactions
205(4)
9.9 Modified Becke-Johnson Functional for Vxc
209(1)
9.10 Comparison of Functionals
209(6)
Exercises
213(2)
Part III Important Preliminaries on Atoms
10 Electronic Structure of Atoms
215(15)
10.1 One-Electron Radial Schrodinger Equation
215(2)
10.2 Independent-Particle Equations: Spherical Potentials
217(2)
10.3 Spin-Orbit Interaction
219(1)
10.4 Open-Shell Atoms: Nonspherical Potentials
219(2)
10.5 Example of Atomic States: Transition Elements
221(3)
10.6 Delta-SCF: Electron Addition, Removal, and Interaction Energies
224(1)
10.7 Atomic Sphere Approximation in Solids
225(5)
Exercises
228(2)
11 Pseudopotentials
230(29)
11.1 Scattering Amplitudes and Pseudopotentials
230(3)
11.2 Orthogonalized Plane Waves (OPWs) and Pseudopotentials
233(4)
11.3 Model Ion Potentials
237(1)
11.4 Norm-Conserving Pseudopotentials (NCPPs)
238(3)
11.5 Generation of /-Dependent Norm-Conserving Pseudopotentials
241(4)
11.6 Unscreening and Core Corrections
245(1)
11.7 Transferability and Hardness
246(1)
11.8 Separable Pseudopotential Operators and Projectors
247(1)
11.9 Extended Norm Conservation: Beyond the Linear Regime
248(1)
11.10 Optimized Norm-Conserving Potentials
249(1)
11.11 Ultrasoft Pseudopotentials
250(2)
11.12 Projector Augmented Waves (PAWs): Keeping the Full Wavefunction
252(3)
11.13 Additional Topics
255(4)
Exercises
256(3)
Part IV Determination of Electronic Structure: The Basic Methods
Overview of
Chapters 12-18
259(3)
12 Plane Waves and Grids: Basics
262(21)
12.1 The Independent-Particle Schrodinger Equation in a Plane Wave Basis
262(2)
12.2 Bloch Theorem and Electron Bands
264(1)
12.3 Nearly-Free-Electron Approximation
265(2)
12.4 Form Factors and Structure Factors
267(2)
12.5 Approximate Atomic-Like Potentials
269(1)
12.6 Empirical Pseudopotential Method (EPM)
270(2)
12.7 Calculation of Electron Density: Introduction of Grids
272(2)
12.8 Real-Space Methods I: Finite Difference and Discontinuous Galerikin Methods
274(3)
12.9 Real-Space Methods II: Multiresolution Methods
277(6)
Exercises
280(3)
13 Plane Waves and Real-Space Methods: Full Calculations
283(12)
13.1 Ab initio Pseudopotential Method
284(2)
13.2 Approach to Self-Consistency and Dielectric Screening
286(1)
13.3 Projector Augmented Waves (PAWs)
287(1)
13.4 Hybrid Functionals and Hartree-Fock in Plane Wave Methods
288(1)
13.5 Supercells: Surfaces, Interfaces, Molecular Dynamics
289(3)
13.6 Clusters and Molecules
292(1)
13.7 Applications of Plane Wave and Grid Methods
292(3)
Exercises
293(2)
14 Localized Orbitals: Tight-Binding
295(25)
14.1 Localized Atom-Centered Orbitals
296(1)
14.2 Matrix Elements with Atomic-Like Orbitals
297(4)
14.3 Spin-Orbit Interaction
301(1)
14.4 Slater-Koster Two-Center Approximation
302(1)
14.5 Tight-Binding Bands: Example of a Single's Band
303(2)
14.6 Two-Band Models
305(1)
14.7 Graphene
306(2)
14.8 Nanotubes
308(2)
14.9 Square Lattice and C11O2 Planes
310(1)
14.10 Semiconductors and Transition Metals
311(1)
14.11 Total Energy, Force, and Stress in Tight-Binding
312(3)
14.12 Transferability: Nonorthogonality and Environment Dependence
315(5)
Exercises
317(3)
15 Localized Orbitals: Full Calculations
320(12)
15.1 Solution of Kohn-Sham Equations in Localized Bases
320(2)
15.2 Analytic Basis Functions: Gaussians
322(2)
15.3 Gaussian Methods: Ground-State and Excitation Energies
324(1)
15.4 Numerical Orbitals
324(3)
15.5 Localized Orbitals: Total Energy, Force, and Stress
327(2)
15.6 Applications of Numerical Local Orbitals
329(1)
15.7 Green's Function and Recursion Methods
329(1)
15.8 Mixed Basis
330(2)
Exercises
331(1)
16 Augmented Functions: APW, KKR, MTO
332(33)
16.1 Augmented Plane Waves (APWs) and "Muffin Tins"
332(5)
16.2 Solving APW Equations: Examples
337(5)
16.3 The KKR or Multiple-Scattering Theory (MST) Method
342(7)
16.4 Alloys and the Coherent Potential Approximation (CPA)
349(1)
16.5 Muffin-Tin Orbitals (MTOs)
350(2)
16.6 Canonical Bands
352(6)
16.7 Localized "Tight-Binding," MTO, and KKR Formulations
358(2)
16.8 Total Energy, Force, and Pressure in Augmented Methods
360(5)
Exercises
362(3)
17 Augmented Functions: Linear Methods
365(21)
17.1 Linearization of Equations and Linear Methods
365(1)
17.2 Energy Derivative of the Wavefunction: i/r and if
366(2)
17.3 General Form of Linearized Equations
368(2)
17.4 Linearized Augmented Plane Waves (LAPWs)
370(2)
17.5 Applications of the LAPW Method
372(3)
17.6 Linear Muffin-Tin Orbital (LMTO) Method
375(4)
17.7 Tight-Binding Formulation
379(1)
17.8 Applications of the LMTO Method
379(2)
17.9 Beyond Linear Methods: NMTO
381(2)
17.10 Full Potential in Augmented Methods
383(3)
Exercises
385(1)
18 Locality and Linear-Scaling O(N) Methods
386(25)
18.1 What Is the Problem?
386(2)
18.2 Locality in Many-Body Quantum Systems
388(2)
18.3 Building the Hamiltonian
390(1)
18.4 Solution of Equations: Nonvariational Methods
391(9)
18.5 Variational Density Matrix Methods
400(2)
18.6 Variational (Generalized) Wannier Function Methods
402(3)
18.7 Linear-Scaling Self-Consistent Density Functional Calculations
405(1)
18.8 Factorized Density Matrix for Large Basis Sets
406(1)
18.9 Combining the Methods
407(4)
Exercises
408(3)
Part V From Electronic Structure to Properties of Matter
19 Quantum Molecular Dynamics (QMD)
411(16)
19.1 Molecular Dynamics (MD): Forces from the Electrons
411(2)
19.2 Born-Oppenheimer Molecular Dynamics
413(1)
19.3 Car-Parrinello Unified Algorithm for Electrons and Ions
414(4)
19.4 Expressions for Plane Waves
418(1)
19.5 Non-self-consistent QMD Methods
419(1)
19.6 Examples of Simulations
419(8)
Exercises
424(3)
20 Response Functions: Phonons and Magnons
427(19)
20.1 Lattice Dynamics from Electronic Structure Theory
427(3)
20.2 The Direct Approach: "Frozen Phonons," Magnons
430(3)
20.3 Phonons and Density Response Functions
433(2)
20.4 Green's Function Formulation
435(1)
20.5 Variational Expressions
436(2)
20.6 Periodic Perturbations and Phonon Dispersion Curves
438(1)
20.7 Dielectric Response Functions, Effective Charges
439(2)
20.8 Electron-Phonon Interactions and Superconductivity
441(1)
20.9 Magnons and Spin Response Functions
442(4)
Exercises
444(2)
21 Excitation Spectra and Optical Properties
446(19)
21.1 Overview
446(1)
21.2 Time-Dependent Density Functional Theory (TDDFT)
447(1)
21.3 Dielectric Response for Noninteracting Particles
448(2)
21.4 Time-Dependent DFT and Linear Response
450(1)
21.5 Time-Dependent Density-Functional Perturbation Theory
451(1)
21.6 Explicit Real-Time Calculations
452(2)
21.7 Optical Properties of Molecules and Clusters
454(5)
21.8 Optical Properties of Crystals
459(4)
21.9 Beyond the Adiabatic Approximation
463(2)
Exercises
464(1)
22 Surfaces, Interfaces, and Lower-Dimensional Systems
465(16)
22.1 Overview
465(1)
22.2 Potential at a Surface or Interface
466(1)
22.3 Surface States: Tamm and Shockley
467(3)
22.4 Shockley States on Metals: Gold (111) Surface
470(1)
22.5 Surface States on Semiconductors
471(1)
22.6 Interfaces: Semiconductors
472(2)
22.7 Interfaces: Oxides
474(3)
22.8 Layer Materials
477(1)
22.9 One-Dimensional Systems
478(3)
Exercises
479(2)
23 Wannier Functions
481(18)
23.1 Definition and Properties
481(4)
23.2 Maximally Projected Wannier Functions
485(2)
23.3 Maximally Localized Wannier Functions
487(4)
23.4 Nonorthogonal Localized Functions
491(1)
23.5 Wannier Functions for Entangled Bands
492(2)
23.6 Hybrid Wannier Functions
494(1)
23.7 Applications
495(4)
Exercises
496(3)
24 Polarization, Localization, and Berry Phases
499(18)
24.1 Overview
499(2)
24.2 Polarization: The Fundamental Difficulty
501(4)
24.3 Geometric Berry Phase Theory of Polarization
505(3)
24.4 Relation to Centers of Wannier Functions
508(1)
24.5 Calculation of Polarization in Crystals
509(1)
24.6 Localization: A Rigorous Measure
510(2)
24.7 The Thouless Quantized Particle Pump
512(1)
24.8 Polarization Lattice
513(4)
Exercises
514(3)
Part VI Electronic Structure and Topology
25 Topology of the Electronic Structure of a Crystal: Introduction
517(14)
25.1 Introduction
517(2)
25.2 Topology of What?
519(1)
25.3 Bulk-Boundary Correspondence
520(1)
25.4 Berry Phase and Topology for Bloch States in the Brillouin Zone
521(3)
25.5 Berry Flux and Chern Numbers: Winding of the Berry Phase
524(2)
25.6 Time-Reversal Symmetry and Topology of the Electronic System
526(1)
25.7 Surface States and the Relation to the Quantum Hall Effect
527(1)
25.8 Wannier Functions and Topology
528(1)
25.9 Topological Quantum Chemistry
529(1)
25.10 Majorana Modes
529(2)
Exercises
530(1)
26 Two-Band Models: Berry Phase, Winding, and Topology
531(16)
26.1 General Formulation for Two Bands
531(2)
26.2 Two-Band Models in One-Space Dimension
533(2)
26.3 Shockley Transition in the Bulk Band Structure and Surface States
535(2)
26.4 Winding of the Hamiltonian in One Dimension: Berry Phase and the Shockley Transition
537(2)
26.5 Winding of the Berry Phase in Two Dimensions: Chern Numbers and Topological Transitions
539(2)
26.6 The Thouless Quantized Particle Pump
541(2)
26.7 Graphene Nanoribbons and the Two-Site Model
543(4)
Exercises
545(2)
27 Topological Insulators I: Two Dimensions
547(22)
27.1 Two Dimensions: sp2 Models
548(2)
27.2 Chern Insulator and Anomalous Quantum Hall Effect
550(2)
27.3 Spin-Orbit Interaction and the Diagonal Approximation
552(2)
27.4 Topological Insulators and the Z2 Topological Invariant
554(3)
27.5 Example of a Topological Insulator on a Square Lattice
557(3)
27.6 From Chains to Planes: Example of a Topological Transition
560(1)
27.7 Hg/CdTe Quantum Well Structures
561(2)
27.8 Graphene and the Two-Site Model
563(4)
27.9 Honeycomb Lattice Model with Large Spin-Orbit Interaction
567(2)
Exercises
567(2)
28 Topological Insulators II: Three Dimensions
569(12)
28.1 Weak and Strong Topological Insulators in Three Dimensions: Four Topological Invariants
569(3)
28.2 Tight-Binding Example in 3D
572(1)
28.3 Normal and Topological Insulators in Three Dimensions: Sb2Se3 and Bi2Se3
573(2)
28.4 Weyl and Dirac Semimetals
575(3)
28.5 Fermi Arcs
578(3)
Exercises
580(1)
Part VII Appendices
Appendix A Functional Equations
581(1)
A.1 Basic Definitions and Variational Equations
581(1)
A.2 Functionals in Density Functional Theory Including Gradients
582(2)
Exercises
583(1)
Appendix B LSDA and GGA Functionals
584(1)
B.1 Local Spin Density Approximation (LSDA)
584(1)
B.2 Generalized-Gradient Approximation (GGAs)
585(1)
B.3 GGAs: Explicit PBE Form
585(2)
Appendix C Adiabatic Approximation
587(1)
C.1 General Formulation
587(2)
C.2 Electron-Phonon Interactions
589(1)
Exercises
589(1)
Appendix D Perturbation Theory, Response Functions, and Green's Functions
590(1)
D.1 Perturbation Theory
590(1)
D.2 Static Response Functions
591(1)
D.3 Response Functions in Self-Consistent Field Theories
592(1)
D.4 Dynamic Response and Kramers-Kronig Relations
593(3)
D.5 Green's Functions
596(1)
D.6 The "2n + 1 Theorem"
597(3)
Exercises
599(1)
Appendix E Dielectric Functions and Optical Properties
600(1)
E.1 Electromagnetic Waves in Matter
600(2)
E.2 Conductivity and Dielectric Tensors
602(1)
E.3 The /Sum Rule
602(1)
E.4 Scalar Longitudinal Dielectric Functions
603(1)
E.5 Tensor Transverse Dielectric Functions
604(1)
E.6 Lattice Contributions to Dielectric Response
605(2)
Exercises
606(1)
Appendix F Coulomb Interactions in Extended Systems
607(1)
F.1 Basic Issues
607(2)
F.2 Point Charges in a Background: Ewald Sums
609(4)
F.3 Smeared Nuclei or Ions
613(1)
F.4 Energy Relative to Neutral Atoms
614(1)
F.5 Surface and Interface Dipoles
615(1)
F.6 Reducing Effects of Artificial Image Charges
616(4)
Exercises
619(1)
Appendix G Stress from Electronic Structure
620(1)
G.1 Macroscopic Stress and Strain
620(3)
G.2 Stress from Two-Body Pair-Wise Forces
623(1)
G.3 Expressions in Fourier Components
623(2)
G.4 Internal Strain
625(2)
Exercises
626(1)
Appendix H Energy and Stress Densities
627(1)
H.1 Energy Density
628(4)
H.2 Stress Density
632(1)
H.3 Integrated Quantities
633(1)
H.4 Electron Localization Function (ELF)
634(3)
Exercises
636(1)
Appendix I Alternative Force Expressions
637(1)
I.1 Variational Freedom and Forces
638(2)
I.2 Energy Differences
640(1)
I.3 Pressure
640(1)
I.4 Force and Stress
641(1)
I.5 Force in APW-Type Methods
642(2)
Exercises
643(1)
Appendix J Scattering and Phase Shifts
644(1)
J.1 Scattering and Phase Shifts for Spherical Potentials
644(3)
Appendix K Useful Relations and Formulas
647(1)
K.1 Bessel, Neumann, and Hankel Functions
647(1)
K.2 Spherical Harmonics and Legendre Polynomials
648(1)
K.3 Real Spherical Harmonics
649(1)
K.4 Clebsch-Gordon and Gaunt Coefficients
649(1)
K.5 Chebyshev Polynomials
650(1)
Appendix L Numerical Methods
651(1)
L.1 Numerical Integration and the Numerov Method
651(1)
L.2 Steepest Descent
652(1)
L.3 Conjugate Gradient
653(2)
L.4 Quasi-Newton-Raphson Methods
655(1)
L.5 Pulay DIIS Full-Subspace Method
655(1)
L.6 Broyden Jacobian Update Methods
656(1)
L.7 Moments, Maximum Entropy, Kernel Polynomial Method, and Random Vectors
657(4)
Exercises
659(2)
Appendix M Iterative Methods in Electronic Structure
661(1)
M.1 Why Use Iterative Methods?
661(1)
M.2 Simple Relaxation Algorithms
662(1)
M.3 Preconditioning
663(1)
M.4 Iterative (Krylov) Subspaces
664(1)
M.5 The Lanczos Algorithm and Recursion
665(2)
M.6 Davidson Algorithms
667(1)
M.7 Residual Minimization in the Subspace - RMM-DIIS
667(1)
M.8 Solution by Minimization of the Energy Functional
668(4)
M.9 Comparison/Combination of Methods: Minimization of Residual or Energy
672(1)
M.10 Exponential Projection in Imaginary Time
672(1)
M.11 Algorithmic Complexity: Transforms and Sparse Hamiltonians
672(5)
Exercises
676(1)
Appendix N Two-Center Matrix Elements: Expressions for Arbitrary Angular Momentum
677(2)
Appendix O Dirac Equation and Spin-Orbit Interaction
679(1)
O.1 The Dirac Equation
680(1)
O.2 The Spin-Orbit Interaction in the Schrodinger Equation
681(2)
O.3 Relativistic Equations and Calculation of the Spin-Orbit Interaction in an Atom
683(3)
Appendix P Berry Phase, Curvature, and Chern Numbers
686(1)
P.1 Overview
686(1)
P.2 Berry Phase and Berry Connection
687(2)
P.3 Berry Flux and Curvature
689(2)
P.4 Chern Number and Topology
691(1)
P.5 Adiabatic Evolution
692(1)
P.6 Aharonov-Bohm Effect
692(2)
P.7 Dirac Magnetic Monopoles and Chern Number
694(3)
Exercises
696(1)
Appendix Q Quantum Hall Effect and Edge Conductivity
697(1)
Q.1 Quantum Hall Effect and Topology
697(1)
Q.2 Nature of the Surface States in the QHE
698(3)
Appendix R Codes for Electronic Structure Calculations for Solids
701(3)
References 704(52)
Index 756
Richard M. Martin is Emeritus Professor of Physics at the University of Illinois Urbana-Champaign and Adjunct Professor of Applied Physics at Stanford University. He has made important contributions to many areas of modern electronic structure, including over 200 papers and is a co-author of another major book in the field, Interacting Electrons: Theory and Computational Approaches. (Cambridge University Press, 2016)
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