Modern Condensed Matter Physics

Citation

Girvin, S. M., & Yang, K. (2019). Modern Condensed Matter Physics. Cambridge University Press.

Chapter Summary

The book has 20 chapters and ten appendices in about 700 pages, plus a preface and a reference list. The publisher presents it as a comprehensive graduate textbook that brings together the most important advances of recent decades and prepares students for research or for reading more advanced literature. It covers the basics of crystalline solids and their analogues (optical lattices and photonic crystals), and cutting-edge topics: disordered systems, mesoscopic systems, many-body systems, quantum magnetism, Bose–Einstein condensates, quantum entanglement and superconducting quantum bits, with the mathematical background needed for topological concepts. Exercises, commentary boxes and appendices are provided.

Chapter 1: Overview of Condensed Matter Physics

A short opening survey of the field, about eight pages, before the technical chapters begin.

Chapters 2–4: Spatial Structure; Lattices and Symmetries; Neutron Scattering

The structural foundation: how spatial structure is described, the symmetries of lattices, and neutron scattering as a probe of structure.

Chapters 5–6: Dynamics of Lattice Vibrations; Quantum Theory of Harmonic Crystals

Lattice dynamics, first as vibrations of the crystal and then in its quantum treatment.

Chapters 7–9: Electronic Structure of Crystals; Semiclassical Transport Theory; Semiconductors

The longest early chapter, on electronic structure (about 65 pages), is followed by semiclassical transport and a chapter on semiconductors. Together these cover the traditional core of solid state physics for electrons.

Chapters 10–12: Non-local Transport in Mesoscopic Systems; Anderson Localization; Integer Quantum Hall Effect

The first modern block: transport on mesoscopic scales, localization by disorder (a long chapter of about 50 pages), and the integer quantum Hall effect.

Chapters 13–14: Topology and Berry Phase; Topological Insulators and Semimetals

The mathematical concepts of topology and Berry phase, then their application to topological insulators and semimetals. The appendices include a brief primer on topology.

Chapters 15–16: Interacting Electrons; Fractional Quantum Hall Effect

Electron-electron interactions in solids and the fractional quantum Hall effect, each a long chapter (about 55 and 50 pages).

Chapters 17–18: Magnetism; Bose–Einstein Condensation and Superfluidity

Magnetism is treated at length (about 50 pages), followed by a shorter chapter on Bose–Einstein condensation and superfluidity.

Chapters 19–20: Superconductivity: Basic Phenomena and Phenomenological Theories; Microscopic Theory of Superconductivity

Superconductivity closes the main text, first through phenomena and phenomenological theories and then through the microscopic theory. Appendices follow on linear-response theory, the Poisson summation formula, tunneling and scanning tunneling microscopy, a primer on topology, scattering matrices, quantum entanglement, noise in electrical circuits, functional differentiation, low-energy effective Hamiltonians and second quantization.

Key Concepts

• Spatial structure and lattice symmetry: spatial structure, lattice symmetry and neutron scattering (Chapters 2–4).
• Phonons: classical and quantum theory of lattice vibrations (Chapters 5–6).
• Semiclassical transport: electron dynamics in crystals (Chapter 8).
• Mesoscopic transport and Anderson localization: non-local transport and disorder effects (Chapters 10–11).
• Quantum Hall effects: integer and fractional (Chapters 12 and 16).
• Berry phase and topological insulators: topology applied to band structure (Chapters 13–14).
• Interacting electrons: many-body effects (Chapter 15).
• Magnetism and superconductivity: Chapters 17, 19 and 20.

Critical Analysis

Strengths

• Modern selection of topics. The publisher emphasises recent advances: topological phases, quantum Hall physics, mesoscopic transport, quantum entanglement and superconducting quantum bits sit beside the standard material, so the book spans both the foundations and current research themes.
• Mathematical support for topology. The publisher notes that appropriate mathematical background is provided for the topological concepts now common in the field; the contents include chapters on topology and Berry phase and an appendix with a primer on topology.
• Aids for different readers. Exercises, commentary boxes and appendices are described as giving guidance and feedback for both beginners and experts, and appendices such as an introduction to second quantization back up the main text.
• Scope beyond crystals. The book includes optical lattices and photonic crystals as analogues of solids.

Limitations

• Size. At about 700 pages and 20 chapters, the book supplies material for more than one graduate course, so instructors and readers need to choose chapters.
• Uneven chapter lengths. Chapters range from about 8 pages (the overview) to about 65 (electronic structure of crystals), and the chapters on localization, interacting electrons, the fractional quantum Hall effect and magnetism each run to roughly 50 pages, so the pace is not uniform.
• Many-body prerequisites. The site lists introductory second quantization as a prerequisite, although the book supplies an appendix on it; readers without any exposure should read that appendix first.

Where It Fits in the Course

Girvin and Yang is the graduate-level text in the condensed matter list, and the natural step after an undergraduate solid state course. Kittel's Introduction to Solid State Physics is the long-established general undergraduate text, and Hofmann's Solid State Physics: An Introduction, Hook and Hall's Solid State Physics and Simon's The Oxford Solid State Basics are shorter introductory courses. Ibach and Lüth's Solid-State Physics adds a materials-science and experimental emphasis. Girvin and Yang covers much of the same ground (structure, phonons, band theory, transport, magnetism, superconductivity) but at a more advanced level, and adds mesoscopic physics, topological phases and the quantum Hall effects.

A sensible route is one of the introductory books first, then Girvin and Yang; students who want the traditional topics only can stop at Kittel.

How to Use This Book

The book is for graduate students (CUP describes it as for senior or first-year graduate level) who have undergraduate solid state physics, quantum mechanics and statistical mechanics.

A practical plan: Chapters 2–9 revise and extend the standard solid-state foundation and can be read quickly by those who have taken a good undergraduate course. The distinctive core is Chapters 10–16 (mesoscopic transport, localization, quantum Hall effects, topology and interacting electrons), which deserve careful reading with exercises. Chapters 17–20 on magnetism and superconductivity can be chosen as needed. Use the appendices as short reference chapters for second quantization, linear response and topology, and read the commentary boxes as they appear.