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E-raamat: Modern Condensed Matter Physics

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(Yale University, Connecticut), (Florida State University)
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  • Ilmumisaeg: 28-Feb-2019
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108573610
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Modern Condensed Matter PhysicsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 28-Feb-2019
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108573610
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Modern Condensed Matter Physics brings together the most important advances in the field of recent decades. It provides instructors teaching graduate-level condensed matter courses with a comprehensive and in-depth textbook that will prepare graduate students for research or further study as well as reading more advanced and specialized books and research literature in the field. This textbook covers the basics of crystalline solids as well as analogous optical lattices and photonic crystals, while discussing cutting-edge topics such as disordered systems, mesoscopic systems, many-body systems, quantum magnetism, Bose–Einstein condensates, quantum entanglement, and superconducting quantum bits. Students are provided with the appropriate mathematical background to understand the topological concepts that have been permeating the field, together with numerous physical examples ranging from the fractional quantum Hall effect to topological insulators, the toric code, and majorana fermions. Exercises, commentary boxes, and appendices afford guidance and feedback for beginners and experts alike.

This modern textbook offers graduate students a comprehensive and accessible route from fundamental concepts to modern topics, language, and methods in the field. Coverage includes disordered and mesoscopic systems, quantum magnetism, Bose–Einstein condensates, superconductivity, and quantum entanglement. It is an ideal reference for researchers.

Arvustused

'Finally, an excellent introductory graduate text for the modern era of quantum condensed matter physics! Girvin and Yang deftly describe the transformative advances in the field, highlighting the close connection between theory and experiment. Highly recommended to all, from physics students to researchers seeking to reset their foundations.' Subir Sachdev, Harvard University, Massachusetts 'This book is a milestone for condensed matter physics that covers the field from Bragg scattering to superconductivity and topology of the electronic band structure with clarity and depth. It is an inspiring text and a reference for anyone in the field.' Richard Martin, University of Illinois

Muu info

Comprehensive and accessible coverage from the basics to advanced topics in modern quantum condensed matter physics.
Preface xvii
Acknowledgments xix
1 Overview of Condensed Matter Physics 1(8)
1.1 Definition of Condensed Matter and Goals of Condensed Matter Physics
1(2)
1.2 Classification (or Phases) of Condensed Matter Systems
3(3)
1.2.1 Atomic Spatial Structures
4(1)
1.2.2 Electronic Structures or Properties
4(1)
1.2.3 Symmetries
5(1)
1.2.4 Beyond Symmetries
6(1)
1.3 Theoretical Descriptions of Condensed Matter Phases
6(2)
1.4 Experimental Probes of Condensed Matter Systems
8(1)
2 Spatial Structure 9(11)
2.1 Probing the Structure
9(1)
2.2 Semiclassical Theory of X-Ray Scattering
10(3)
2.3 Quantum Theory of Electron-Photon Interaction and X-Ray Scattering
13(2)
2.4 X-Ray Scattering from a Condensed Matter System
15(1)
2.5 Relationship of S(q) and Spatial Correlations
16(1)
2.6 Liquid State versus Crystal State
17(3)
3 Lattices and Symmetries 20(24)
3.1 The Crystal as a Broken-Symmetry State
20(4)
3.2 Bravais Lattices and Lattices with Bases
24(6)
3.2.1 Bravais Lattices
24(2)
3.2.2 Lattices with Bases
26(3)
3.2.3 Lattice Symmetries in Addition to Translation
29(1)
3.3 Reciprocal Lattices
30(4)
3.4 X-Ray Scattering from Crystals
34(4)
3.5 Effects of Lattice Fluctuations on X-Ray Scattering
38(3)
3.6 Notes and Further Reading
41(3)
4 Neutron Scattering 44(20)
4.1 Introduction to Neutron Scattering
44(2)
4.2 Inelastic Neutron Scattering
46(4)
4.3 Dynamical Structure Factor and f-Sum Rule
50(10)
4.3.1 Classical Harmonic Oscillator
54(2)
4.3.2 Quantum Harmonic Oscillator
56(4)
4.4 Single-Mode Approximation and Superfluid 4He
60(4)
5 Dynamics of Lattice Vibrations 64(14)
5.1 Elasticity and Sound Modes in Continuous Media
64(4)
5.2 Adiabatic Approximation and Harmonic Expansion of Atomic Potential
68(3)
5.3 Classical Dynamics of Lattice Vibrations
71(7)
6 Quantum Theory of Harmonic Crystals 78(20)
6.1 Heat Capacity
78(5)
6.2 Canonical Quantization of Lattice Vibrations
83(5)
6.3 Quantum Dynamical Structure Factor
88(3)
6.4 Debye-Waller Factor and Stability of Crystalline Order
91(2)
6.5 Mossbauer Effect
93(5)
7 Electronic Structure of Crystals 98(66)
7.1 Drude Theory of Electron Conduction in Metals
98(6)
7.2 Independent Electron Model
104(1)
7.3 Bloch's Theorem
105(12)
7.3.1 Band Gaps and Bragg Reflection
114(1)
7.3.2 Van Hove Singularities
115(1)
7.3.3 Velocity of Bloch Electrons
116(1)
7.4 Tight-Binding Method
117(16)
7.4.1 Bonds vs. Bands
122(1)
7.4.2 Wannier Functions
122(2)
7.4.3 Continuum Limit of Tight-Binding Hamiltonians
124(2)
7.4.4 Limitations of the Tight-Binding Model
126(3)
7.4.5 s-d Hybridization in Transition Metals
129(4)
7.5 Graphene Band Structure
133(5)
7.6 Polyacetylene and the Su-Schrieffer-Heeger Model
138(10)
7.6.1 Dirac electrons in 1D and the Peierls instability
138(4)
7.6.2 Ground-State Degeneracy and Solitons
142(2)
7.6.3 Zero Modes Bound to Solitons
144(3)
7.6.4 Quantum Numbers of Soliton States and Spin-Charge Separation
147(1)
7.7 Thermodynamic Properties of Bloch Electrons
148(5)
7.7.1 Specific Heat
149(1)
7.7.2 Magnetic Susceptibility
150(3)
7.8 Spin-Orbit Coupling and Band Structure
153(3)
7.9 Photonic Crystals
156(3)
7.10 Optical Lattices
159(5)
7.10.1 Oscillator Model of Atomic Polarizability
160(2)
7.10.2 Quantum Effects in Optical Lattices
162(2)
8 Semiclassical Transport Theory 164(34)
8.1 Review of Semiclassical Wave Packets
164(1)
8.2 Semiclassical Wave-Packet Dynamics in Bloch Bands
165(6)
8.2.1 Derivation of Bloch Electron Equations of Motion
169(2)
8.2.2 Zener Tunneling (or Interband Transitions)
171(1)
8.3 Holes
171(2)
8.4 Uniform Magnetic Fields
173(3)
8.5 Quantum Oscillations
176(3)
8.6 Semiclassical E x B Drift
179(2)
8.7 The Boltzmann Equation
181(5)
8.8 Boltzmann Transport
186(7)
8.8.1 Einstein Relation
191(2)
8.9 Thermal Transport and Thermoelectric Effects
193(5)
9 Semiconductors 198(24)
9.1 Homogeneous Bulk Semiconductors
198(6)
9.2 Impurity Levels
204(3)
9.3 Optical Processes in Semiconductors
207(5)
9.3.1 Angle-Resolved Photoemission Spectroscopy
210(2)
9.4 The p-n Junction
212(4)
9.4.1 Light-Emitting Diodes and Solar Cells
215(1)
9.5 Other Devices
216(5)
9.5.1 Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs)
216(1)
9.5.2 Heterostructures
217(3)
9.5.3 Quantum Point Contact, Wire and Dot
220(1)
9.6 Notes and Further Reading
221(1)
10 Non-local Transport in Mesoscopic Systems 222(30)
10.1 Introduction to Transport of Electron Waves
222(3)
10.2 Landauer Formula and Conductance Quantization
225(6)
10.3 Multi-terminal Devices
231(2)
10.4 Universal Conductance Fluctuations
233(5)
10.4.1 Transmission Eigenvalues
238(2)
10.4.2 UCF Fingerprints
240(2)
10.5 Noise in Mesoscopic Systems
242(6)
10.5.1 Quantum Shot Noise
245(3)
10.6 Dephasing
248(4)
11 Anderson Localization 252(49)
11.1 Absence of Diffusion in Certain Random Lattices
253(3)
11.2 Classical Diffusion
256(2)
11.3 Semiclassical Diffusion
258(9)
11.3.1 Review of Scattering from a Single Impurity
258(4)
11.3.2 Scattering from Many Impurities
262(3)
11.3.3 Multiple Scattering and Classical Diffusion
265(2)
11.4 Quantum Corrections to Diffusion
267(4)
11.4.1 Real-Space Picture
268(1)
11.4.2 Enhanced Backscattering
269(2)
11.5 Weak Localization in 2D
271(4)
11.5.1 Magnetic Fields and Spin-Orbit Coupling
273(2)
11.6 Strong Localization in 1D
275(2)
11.7 Localization and Metal-Insulator Transition in 3D
277(2)
11.8 Scaling Theory of Localization and the Metal-Insulator Transition
279(8)
11.8.1 Thouless Picture of Conductance
279(3)
11.8.2 Persistent Currents in Disordered Mesoscopic Rings
282(1)
11.8.3 Scaling Theory
283(1)
11.8.4 Scaling Hypothesis and Universality
284(3)
11.9 Scaling and Transport at Finite Temperature
287(7)
11.9.1 Mobility Gap and Activated Transport
291(1)
11.9.2 Variable-Range Hopping
292(2)
11.10 Anderson Model
294(3)
11.11 Many-Body Localization
297(4)
12 Integer Quantum Hall Effect 301(30)
12.1 Hall-Effect Transport in High Magnetic Fields
301(3)
12.2 Why 2D Is Important
304(1)
12.3 Why Disorder and Localization Are Important
305(1)
12.4 Classical and Semiclassical Dynamics
306(3)
12.4.1 Classical Dynamics
306(2)
12.4.2 Semiclassical Approximation
308(1)
12.5 Quantum Dynamics in Strong B Fields
309(6)
12.6 IQHE Edge States
315(3)
12.7 Semiclassical Percolation Picture of the IQHE
318(3)
12.8 Anomalous Integer Quantum Hall Sequence in Graphene
321(3)
12.9 Magnetic Translation Invariance and Magnetic Bloch Bands
324(5)
12.9.1 Simple Landau Gauge Example
327(2)
12.10 Quantization of the Hall Conductance in Magnetic Bloch Bands
329(2)
13 Topology and Berry Phase 331(31)
13.1 Adiabatic Evolution and the Geometry of Hilbert Space
331(5)
13.2 Berry Phase and the Aharonov-Bohm Effect
336(3)
13.3 Spin-1/2 Berry Phase
339(5)
13.3.1 Spin-Orbit Coupling and Suppression of Weak Localization
343(1)
13.4 Berry Curvature of Bloch Bands and Anomalous Velocity
344(4)
13.4.1 Anomalous Velocity
345(3)
13.5 Topological Quantization of Hall Conductance of Magnetic Bloch Bands
348(8)
13.5.1 Wannier Functions of Topologically Non-trivial Bands
351(1)
13.5.2 Band Crossing and Change of Band Topology
352(1)
13.5.3 Relation Between the Chern Number and Chiral Edge States: Bulk-Edge Correspondence
353(3)
13.6 An Example of Bands Carrying Non-zero Chern Numbers: Haldane Model
356(2)
13.7 Thouless Charge Pump and Electric Polarization
358(4)
13.7.1 Modern Theory of Electric Polarization
360(2)
14 Topological Insulators and Semimetals 362(14)
14.1 Kane-Mele Model
362(2)
14.2 Integers2 Characterization of Topological Insulators
364(4)
14.3 Massless Dirac Surface/Interface States
368(3)
14.4 Weyl Semimetals
371(4)
14.4.1 Fermi Arcs on the Surface
372(1)
14.4.2 Chiral Anomaly
373(2)
14.5 Notes and Further Reading
375(1)
15 Interacting Electrons 376(54)
15.1 Hartree Approximation
376(2)
15.2 Hartree-Fock Approximation
378(4)
15.2.1 Koopmans' Theorem
381(1)
15.3 Hartree-Fock Approximation for the 3D Electron Gas
382(3)
15.3.1 Total Exchange Energy of the 3DEG in the Hartree-Fock Approximation
384(1)
15.4 Density Functional Theory
385(2)
15.5 Kohn-Sham Single-Particle Equations
387(2)
15.6 Local-Density Approximation
389(2)
15.7 Density-Density Response Function and Static Screening
391(5)
15.7.1 Thomas-Fermi Approximation
394(1)
15.7.2 Lindhard Approximation
394(2)
15.8 Dynamical Screening and Random-Phase Approximation
396(1)
15.9 Plasma Oscillation and Plasmon Dispersion
397(3)
15.9.1 Plasma Frequency and Plasmon Dispersion from the RPA
397(1)
15.9.2 Plasma Frequency from Classical Dynamics
398(1)
15.9.3 Plasma Frequency and Plasmon Dispersion from the Single-Mode Approximation
399(1)
15.10 Dielectric Function and Optical Properties
400(2)
15.10.1 Dielectric Function and AC Conductivity
400(1)
15.10.2 Optical Measurements of Dielectric Function
401(1)
15.11 Landau's Fermi-Liquid Theory
402(7)
15.11.1 Elementary Excitations of a Free Fermi Gas
402(2)
15.11.2 Adiabaticity and Elementary Excitations of an Interacting Fermi Gas
404(3)
15.11.3 Fermi-Liquid Parameters
407(2)
15.12 Predictions of Fermi-Liquid Theory
409(3)
15.12.1 Heat Capacity
409(1)
15.12.2 Compressibility
410(1)
15.12.3 Spin Susceptibility
411(1)
15.12.4 Collective Modes, Dynamical and Transport Properties
411(1)
15.13 Instabilities of Fermi Liquids
412(8)
15.13.1 Ferromagnetic Instability
412(1)
15.13.2 Pomeranchuk Instabilities
413(1)
15.13.3 Pairing Instability
414(4)
15.13.4 Charge and Spin Density-Wave Instabilities
418(1)
15.13.5 One Dimension
419(1)
15.13.6 Two-Dimensional Electron Gas at High Magnetic Field
420(1)
15.14 Infrared Singularities in Fermi Liquids
420(9)
15.14.1 Perfect Screening and the Friedel Sum Rule
420(2)
15.14.2 Orthogonality Catastrophe
422(1)
15.14.3 Magnetic Impurities in Metals: The Kondo Problem
423(6)
15.15 Summary and Outlook
429(1)
16 Fractional Quantum Hall Effect 430(50)
16.1 Landau Levels Revisited
431(2)
16.2 One-Body Basis States in Symmetric Gauge
433(2)
16.3 Two-Body Problem and Haldane Pseudopotentials
435(3)
16.4 The v = 1 Many-Body State and Plasma Analogy
438(4)
16.4.1 Electron and Hole Excitations at v = 1
441(1)
16.5 Laughlin's Wave Function
442(4)
16.6 Quasiparticle and Quasihole Excitations of Laughlin States
446(6)
16.7 Fractional Statistics of Laughlin Quasiparticles
452(8)
16.7.1 Possibility of Fractional Statistics in 2D
452(3)
16.7.2 Physical Model of Anyons
455(2)
16.7.3 Statistics Angle of Laughlin Quasiholes
457(3)
16.8 Collective Excitations
460(3)
16.9 Bosonization and Fractional Quantum Hall Edge States
463(6)
16.9.1 Shot-Noise Measurement of Fractional Quasiparticle Charge
467(2)
16.10 Composite Fermions and Hierarchy States
469(1)
16.10.1 Another Take on Laughlin's Wave Function
469(1)
16.10.2 Jain Sequences
470(1)
16.11 General Formalism of Electron Dynamics Confined to a Single Landau Level
470(6)
16.11.1 Finite-Size Geometries
474(2)
16.12 Relation between Fractional Statistics and Topological Degeneracy
476(2)
16.13 Notes and Further Reading
478(2)
17 Magnetism 480(51)
17.1 Basics
480(1)
17.2 Classical Theory of Magnetism
481(1)
17.3 Quantum Theory of Magnetism of Individual Atoms
481(5)
17.3.1 Quantum Diamagnetism
482(3)
17.3.2 Quantum Paramagnetism
485(1)
17.3.3 Quantum Spin
486(1)
17.4 The Hubbard Model and Mott Insulators
486(5)
17.5 Magnetically Ordered States and Spin-Wave Excitations
491(8)
17.5.1 Ferromagnets
491(4)
17.5.2 Antiferromagnets
495(4)
17.6 One Dimension
499(14)
17.6.1 Lieb-Schultz-Mattis Theorem
501(1)
17.6.2 Spin-1/2 Chains
502(4)
17.6.3 Spin-1 Chains, Haldane Gap, and String Order
506(4)
17.6.4 Matrix Product and Tensor Network States
510(3)
17.7 Valence-Bond-Solid and Spin-Liquid States in 2D and Higher Dimensions
513(8)
17.7.1 Integers2 Topological Order in Resonating Valence-Bond Spin Liquid
519(2)
17.8 An Exactly Solvable Model of Integers2 Spin Liquid: Kitaev's Toric Code
521(7)
17.8.1 Toric Code as Quantum Memory
525(3)
17.9 Landau Diamagnetism
528(3)
18 Bose-Einstein Condensation and Superfluidity 531(18)
18.1 Non-interacting Bosons and Bose-Einstein Condensation
531(8)
18.1.1 Off-Diagonal Long-Range Order
534(1)
18.1.2 Finite Temperature and Effects of Trapping Potential
535(1)
18.1.3 Experimental Observation of Bose-Einstein Condensation
536(3)
18.2 Weakly Interacting Bosons and Bogoliubov Theory
539(3)
18.3 Stability of Condensate and Superfluidity
542(3)
18.4 Bose-Einstein Condensation of Exciton-Polaritons: Quantum Fluids of Light
545(4)
19 Superconductivity: Basic Phenomena and Phenomenological Theories 549(43)
19.1 Thermodynamics
549(4)
19.1.1 Type-I Superconductors
550(2)
19.1.2 Type-II Superconductors
552(1)
19.2 Electrodynamics
553(3)
19.3 Meissner Kernel
556(2)
19.4 The Free-Energy Functional
558(1)
19.5 Ginzburg-Landau Theory
559(7)
19.6 Type-II Superconductors
566(7)
19.6.1 Abrikosov Vortex Lattice
568(1)
19.6.2 Isolated Vortices
569(4)
19.7 Why Do Superconductors Superconduct?
573(3)
19.8 Comparison between Superconductivity and Superfluidity
576(3)
19.9 Josephson Effect
579(8)
19.9.1 Superconducting Quantum Interference Devices (SQUIDS)
585(2)
19.10 Flux-Flow Resistance in Superconductors
587(1)
19.11 Superconducting Quantum Bits
587(5)
20 Microscopic Theory of Superconductivity 592(40)
20.1 Origin of Attractive Interaction
592(2)
20.2 BCS Reduced Hamiltonian and Mean-Field Solution
594(9)
20.2.1 Condensation Energy
598(1)
20.2.2 Elementary Excitations
599(3)
20.2.3 Finite-Temperature Properties
602(1)
20.3 Microscopic Derivation of Josephson Coupling
603(3)
20.4 Electromagnetic Response of Superconductors
606(3)
20.5 BCS-BEC Crossover
609(2)
20.6 Real-Space Formulation and the Bogoliubov-de Gennes Equation
611(3)
20.7 Kitaev's p-Wave Superconducting Chain and Topological Superconductors
614(3)
20.8 Unconventional Superconductors
617(4)
20.8.1 General Solution of Cooper Problem
617(2)
20.8.2 General Structure of Pairing Order Parameter
619(1)
20.8.3 Fulde-Ferrell-Larkin-Ovchinnikov States
620(1)
20.9 High-Temperature Cuprate Superconductors
621(11)
20.9.1 Antiferromagnetism in the Parent Compound
622(2)
20.9.2 Effects of Doping
624(1)
20.9.3 Nature of the Superconducting State
624(3)
20.9.4 Why d-Wave?
627(5)
Appendix A: Linear-Response Theory 632(8)
A.1 Static Response
632(2)
A.2 Dynamical Response
634(2)
A.3 Causality, Spectral Densities, and Kramers-Kronig Relations
636(4)
Appendix B: The Poisson Summation Formula 640(2)
Appendix C: Tunneling and Scanning Tunneling Microscopy 642(5)
C.1 A Simple Example
642(1)
C.2 Tunnel Junction
643(2)
C.3 Scanning Tunneling Microscopy
645(2)
Appendix D: Brief Primer on Topology 647(10)
D.1 Introduction
647(1)
D.2 Homeomorphism
648(1)
D.3 Homotopy
648(2)
D.4 Fundamental Group
650(1)
D.5 Gauss-Bonnet Theorem
651(3)
D.6 Topological Defects
654(3)
Appendix E: Scattering Matrices, Unitarity, and Reciprocity 657(2)
Appendix F: Quantum Entanglement in Condensed Matter Physics 659(6)
F.1 Reduced Density Matrix
659(2)
F.2 Schmidt and Singular-Value Decompositions
661(1)
F.3 Entanglement Entropy Scaling Laws
662(1)
F.4 Other Measures of Entanglement
663(1)
F.5 Closing Remarks
664(1)
Appendix G: Linear Response and Noise in Electrical Circuits 665(8)
G.1 Classical Thermal Noise in a Resistor
665(3)
G.2 Linear Response of Electrical Circuits
668(2)
G.3 Hamiltonian Description of Electrical Circuits
670(2)
G.3.1 Hamiltonian for Josephson Junction Circuits
672(1)
Appendix H: Functional Differentiation 673(2)
Appendix I: Low-Energy Effective Hamiltonian 675(5)
I.1 Effective Tunneling Hamiltonian
675(2)
I.2 Antiferromagnetism in the Hubbard Model
677(2)
I.3 Summary
679(1)
Appendix J: Introduction to Second Quantization 680(5)
J.1 Second Quantization
680(3)
J.2 Majorana Representation of Fermion Operators
683(2)
References 685(7)
Index 692
Steven M. Girvin received his B.S. in 1971 from Bates College and his Ph.D. in 1977 from Princeton University. He joined the Yale University faculty in 2001, where he is Eugene Higgins Professor of Physics and Professor of Applied Physics. From 2007 to 2017 he served as Deputy Provost for Research. His research interests focus on theoretical condensed matter physics, quantum optics and quantum computation; he is co-developer of the circuit QED paradigm for quantum computation. His honours include: Fellow of American Physical Society, American Association for the Advancement of Science, American Academy of Arts and Sciences; Foreign Member of the Royal Swedish Academy of Sciences, Member US National Academy of Sciences; Oliver E. Buckley Prize of the American Physical Society (2007); Honorary doctorate, Chalmers University of Technology (2017); Conde Award for Teaching Excellence (2003). Kun Yang received his B.S. in 1989 from Fudan University and his Ph.D. in 1994 from Indiana University. He joined the faculty of Florida State University in 1999 where he is now Mckenzie Professor of Physics. His research focuses on many-particle physics in condensed matter and trapped cold atom systems. His honours include: Fellow of American Physical Society, American Association for the Advancement of Science, Alfred Sloan Research Fellowship (1999), Outstanding Young Researcher Award, Overseas Chinese Physics Association (2003).
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