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Advanced Solid State Physics, Second Edition

Book Description

Providing an up-to-date and lucid presentation of phenomena across modern advanced-level solid state physics, this new edition builds on an elementary understanding to introduce students to the key research topics with the minimum of mathematics. It covers cutting-edge topics, including electron transport and magnetism in solids. It is the first book to explain topological insulators and strongly correlated electrons. Explaining solid state physics in a clear and detailed way, it also has over 50 exercises for students to test their knowledge. In addition to the extensive discussion of magnetic impurity problems, bosonization, quantum phase transitions, and disordered systems from the first edition, the new edition includes such topics as topological insulators, high-temperature superconductivity and Mott insulators, renormalization group for Fermi liquids, spontaneous symmetry breaking, zero and finite-temperature Green functions, and the Kubo formalism. Figures from the book and solutions to student exercises are available online at www.cambridge.org/solidstate.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Dedication
  6. Contents
  7. Preface
  8. 1. Introduction
    1. 1.1 Spontaneously broken symmetry
    2. 1.2 Tracking broken symmetry: order parameter
    3. 1.3 Beyond broken symmetry
    4. References
  9. 2. Non-interacting electron gas
    1. Problems
  10. 3. Born–Oppenheimer approximation
    1. 3.1 Basic Hamiltonian
    2. 3.2 Adiabatic approximation
    3. 3.3 Tight-binding approximation
    4. Problem
    5. References
  11. 4. Second quantization
    1. 4.1 Bosons
    2. 4.2 Fermions
    3. 4.3 Fermion operators
    4. Problems
    5. References
  12. 5. Hartree–Fock approximation
    1. 5.1 Non-interacting limit
    2. 5.2 Hartree–Fock approximation
    3. 5.3 Diagrams
    4. Problem
    5. References
  13. 6. Interacting electron gas
    1. 6.1 Uniform electron gas
    2. 6.2 Hartree–Fock excitation spectrum
    3. 6.3 Cohesive energy of metals
    4. Summary
    5. Problems
    6. References
  14. 7. Local magnetic moments in metals
    1. 7.1 Local moments: phenomenology
    2. 7.2 Impurity density of states
    3. 7.3 Green functions
    4. 7.4 Friedel’s sum rule and local moments
    5. Summary
    6. Appendix to Chapter 7: Luttinger’s theorem
    7. Problems
    8. References
  15. 8. Quenching of local moments: the Kondo problem
    1. 8.1 The Kondo Hamiltonian
    2. 8.2 Why is J negative?
    3. 8.3 Scattering and the resistivity minimum
    4. 8.4 Electron–impurity scattering amplitudes
    5. 8.5 Kondo temperature
    6. 8.6 Poor Man’s scaling
    7. Summary
    8. Appendix to Chapter 8: the Schrieffer–Wolff transformation
    9. Problems
    10. References
  16. 9. Screening and plasmons
    1. 9.1 Thomas–Fermi screening
    2. 9.2 Plasma oscillations and collective coordinates
    3. 9.3 Linear response theory
    4. 9.4 Dielectric response function
    5. 9.5 Kubo formula: electrical conductivity
    6. 9.6 Stopping power of a plasma
    7. Summary
    8. Problems
    9. References
  17. 10. Bosonization
    1. 10.1 Luttinger liquid
    2. 10.2 Bosonization of Luttinger model
    3. 10.3 Pair binding: can electrons do it alone?
    4. 10.4 Excitation spectrum
    5. Summary
    6. Problems
    7. References
  18. 11. Electron–lattice interactions
    1. 11.1 Harmonic chain
    2. 11.2 Acoustic phonons
    3. 11.3 Electron–phonon interaction
    4. 11.4 Ultrasonic attenuation
    5. 11.5 Electrical conduction
    6. Summary
    7. Problems
    8. References
  19. 12. Superconductivity in metals
    1. 12.1 Superconductivity: phenomenology
    2. 12.2 Electron–phonon effective interaction
    3. 12.3 Model interaction
    4. 12.4 Cooper pairs
    5. 12.5 Fermi liquid theory
    6. 12.6 Pair amplitude
    7. 12.7 BCS ground state
    8. 12.8 Pair fluctuations
    9. 12.9 Ground state energy
    10. 12.10 Critical magnetic field
    11. 12.11 Energy gap
    12. 12.12 Quasi-particle excitations
    13. 12.13 Thermodynamics
    14. 12.14 Experimental applications
    15. 12.15 Josephson tunneling
    16. Summary
    17. Problems
    18. References
  20. 13. Disorder: localization and exceptions
    1. 13.1 Primer on localization
    2. 13.2 Return probability: localization criterion
    3. 13.3 Weak localization
    4. 13.4 Scaling theory
    5. 13.5 Exceptions to localization
    6. Summary
    7. Problems
    8. References
  21. 14. Quantum phase transitions
    1. 14.1 Quantum rotor model
    2. 14.2 Scaling
    3. 14.3 Mean-field solution
    4. 14.4 Landau–Ginsburg theory
    5. 14.5 Transport properties
    6. 14.6 Experiments
    7. 14.7 Scaling and T-linear resistivity
    8. Problems
    9. References
  22. 15. Quantum Hall and other topological states
    1. 15.1 What is the quantum Hall effect?
    2. 15.2 Landau levels
    3. 15.3 The role of disorder
    4. 15.4 Currents at the edge
    5. 15.5 Topological insulators
    6. 15.6 Laughlin liquid
    7. Summary
    8. Problems
    9. References
  23. 16. Electrons at strong coupling: Mottness
    1. 16.1 Band insulator
    2. 16.2 Mott’s problem
    3. 16.3 Much ado about zeros: Luttinger surface
    4. 16.4 Beyond the atomic limit: Heisenberg versus Slater
    5. 16.5 Dynamical spectral weight transfer
    6. 16.6 Epilogue: 1 = 2 – 1
    7. Problems
    8. References
  24. Index