Chapter 26 Further Reading: QM in Condensed Matter

Tier 1: Essential References

These are the primary references that cover the material of this chapter at a level closely matching our treatment. You should consult at least one.

Ashcroft, N. W. & Mermin, N. D. — Solid State Physics (1976)

The classic graduate-level solid-state textbook. Chapters 8-9 cover Bloch's theorem and the electron gas in a periodic potential (nearly free electron model). Chapters 10-12 cover tight-binding, band structure classification, and semiclassical dynamics. Chapter 34 covers superconductivity. Dense but authoritative, with excellent problems. This book has trained three generations of condensed matter physicists. - Best for: Students who want the complete, rigorous treatment of band theory with all derivations.

Griffiths, D. J. & Schroeter, D. F. — Introduction to Quantum Mechanics, 3rd ed. (2018)

Chapter 5, Section 5.3 covers the band structure problem as an application of identical particles and periodic potentials. The Dirac comb (delta-function Kronig-Penney model) is worked out in detail. Accessible and clear, as always with Griffiths. Section 5.3.2 on Bloch's theorem is concise but complete. - Best for: Students who want a quantum mechanics perspective on band theory (rather than a solid-state perspective). Matches the level of our chapter.

Kittel, C. — Introduction to Solid State Physics, 8th ed. (2005)

The standard undergraduate solid-state text. Chapter 7 covers energy bands, the nearly free electron model, and the Bloch theorem. Chapter 8 covers semiconductor crystals. Chapter 10 covers superconductivity. More accessible than Ashcroft & Mermin but less rigorous. - Best for: Undergraduates who want a gentler introduction with good physical intuition and many experimental examples.

Simon, S. H. — The Oxford Solid State Basics (2013)

A modern undergraduate text that covers the essentials of solid-state physics with exceptional clarity. Chapters 14-16 cover electrons in a periodic potential, band structure, and semiconductors. The treatment is concise, well-motivated, and avoids the encyclopedic style of older texts. - Best for: Students who want a modern, streamlined introduction. Free lecture notes version available online.

Tier 2: Supplementary and Enrichment

These sources provide deeper treatment, alternative perspectives, or advanced topics.

Band Theory and Electronic Structure

Marder, M. P. — Condensed Matter Physics, 2nd ed. (2010) An excellent modern graduate text. Part III (chapters 7-12) covers electronic band structure with a good balance of rigor and physical insight. The treatment of tight-binding models is particularly clear.

Singleton, J. — Band Theory and Electronic Properties of Solids (2001) A focused treatment of band theory at the advanced undergraduate level. Excellent for its detailed coverage of experimental techniques (de Haas-van Alphen, ARPES, optical spectroscopy) that probe band structure. - Best for: Students who want to understand how band structures are measured, not just calculated.

Harrison, W. A. — Electronic Structure and the Properties of Solids (1980, Dover reprint 1989) A unified treatment of electronic structure using the tight-binding method. Harrison's approach — parameterizing all materials via universal tight-binding parameters — is elegant and predictive. Excellent for developing physical intuition about how band structure determines material properties.

Graphene

Castro Neto, A. H. et al. — "The electronic properties of graphene," Reviews of Modern Physics 81, 109 (2009) The definitive review article on graphene physics. Covers the tight-binding band structure, Dirac fermions, Berry phase, quantum Hall effect, transport, disorder, and many-body effects. At 54 pages, it is comprehensive but accessible to advanced undergraduates. - Best for: Anyone who wants to go deep on graphene. Start with Sections I-IV for the band theory.

Katsnelson, M. I. — Graphene: Carbon in Two Dimensions (2012) A monograph on graphene by one of the theoretical pioneers. Combines pedagogical exposition with research-level depth. Chapters 1-3 cover the tight-binding model, Dirac equation, and Berry phase.

Novoselov, K. S. et al. — "Two-dimensional gas of massless Dirac fermions in graphene," Nature 438, 197 (2005) The original experimental paper demonstrating Dirac fermions via the anomalous quantum Hall effect. Short, elegant, and readable.

Superconductivity

Tinkham, M. — Introduction to Superconductivity, 2nd ed. (2004) The standard graduate reference on superconductivity. Chapter 3 covers BCS theory in detail. Chapter 7 covers the Josephson effects. Rigorous but accessible, with excellent physical insight. - Best for: Students who want to understand BCS theory beyond the conceptual level of our chapter.

Schrieffer, J. R. — Theory of Superconductivity (1964, revised 1999) By one of the three creators of BCS theory. Advanced but authoritative. Worth reading Chapter 1 for the historical perspective.

de Gennes, P. G. — Superconductivity of Metals and Alloys (1966, Dover reprint 1999) A classic that introduces the Bogoliubov-de Gennes formalism. More advanced than Tinkham but elegantly written.

Quantum Hall Effect

Girvin, S. M. — "The quantum Hall effect: Novel excitations and broken symmetries," in Topological Aspects of Low Dimensional Systems (1999) An outstanding set of lecture notes covering both the integer and fractional quantum Hall effects. Available on arXiv: cond-mat/9907002. Remarkably clear for such a deep topic. - Best for: Students who want to understand the quantum Hall effect from the ground up, with connections to topology.

Yoshioka, D. — The Quantum Hall Effect (2002) A comprehensive monograph covering Landau levels, IQHE, FQHE, edge states, and composite fermions. Graduate level.

Laughlin, R. B. — "Nobel Lecture: Fractional quantization," Reviews of Modern Physics 71, 863 (1999) Laughlin's Nobel lecture on the fractional quantum Hall effect. Beautifully written and accessible, with deep physical insight into why the FQHE is fundamentally about topology and emergence.

Topological Aspects (Preview of Chapter 36)

Bernevig, B. A. — Topological Insulators and Topological Superconductors (2013) A pedagogical introduction to topological phases of matter, starting from the band theory of this chapter. Chapters 1-5 build from tight-binding models to the Berry phase to topological invariants.

Hasan, M. Z. & Kane, C. L. — "Topological insulators and superconductors," Reviews of Modern Physics 82, 3045 (2010) A comprehensive review of topological insulators. Sections I-III are accessible with the background from this chapter.

Online Resources

MIT OpenCourseWare — 8.231 Physics of Solids I

Covers crystal structure, diffraction, and electronic band structure at the graduate level. Lecture notes and problem sets available. - Best for: Structured self-study of solid-state physics.

Coursera — "Semiconductor Physics" (University of Colorado Boulder)

Covers band theory, doping, p-n junctions, and devices at the introductory level. Video lectures with quizzes. - Best for: Students who want device physics context for the band theory in this chapter.

Feynman Lectures on Physics, Vol. III, Chapters 13-14

Feynman's treatment of propagation in a crystal lattice. He derives the tight-binding band structure using his unique physical reasoning. Free at feynmanlectures.caltech.edu. - Best for: Everyone. Feynman's physical intuition for band formation is unmatched.

3Blue1Brown and MinutePhysics — Various videos on quantum mechanics and condensed matter

Search for "band gap," "semiconductor," "quantum Hall effect" for accessible visual explanations.

Original Papers (for the historically inclined)

  • Bloch, F. (1929). "Uber die Quantenmechanik der Elektronen in Kristallgittern." Zeitschrift fur Physik, 52, 555-600. [The original Bloch theorem paper.]
  • Kronig, R. de L. & Penney, W. G. (1931). "Quantum mechanics of electrons in crystal lattices." Proceedings of the Royal Society A, 130, 499-513.
  • Wallace, P. R. (1947). "The band theory of graphite." Physical Review, 71, 622-634. [Graphene band structure, 57 years before isolation.]
  • Bardeen, J., Cooper, L. N., & Schrieffer, J. R. (1957). "Theory of superconductivity." Physical Review, 108, 1175-1204. [The BCS paper.]
  • von Klitzing, K., Dorda, G., & Pepper, M. (1980). "New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance." Physical Review Letters, 45, 494-497. [Discovery of the IQHE.]
  • Laughlin, R. B. (1983). "Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations." Physical Review Letters, 50, 1395-1398. [Laughlin wavefunction.]
  • Novoselov, K. S. et al. (2004). "Electric field effect in atomically thin carbon films." Science, 306, 666-669. [Isolation of graphene.]
  • Cao, Y. et al. (2018). "Unconventional superconductivity in magic-angle graphene superlattices." Nature, 556, 43-50. [Magic-angle twisted bilayer graphene.]

Reading Strategy

For Chapter 26, we recommend:

  1. Everyone: Read Griffiths Section 5.3 (Dirac comb and Bloch's theorem) for a clean derivation that matches our level. Then read Feynman Lectures III, Ch. 13-14 for unmatched physical insight into band formation.

  2. If you want more on band theory: Read Ashcroft & Mermin, Chapters 8-9 (nearly free electrons) and Chapter 10 (tight-binding). Work through the problems — they are excellent.

  3. If graphene excites you: Read the Castro Neto et al. review (2009), Sections I-IV. Then read the Novoselov et al. (2005) experimental paper.

  4. If superconductivity intrigues you: Read Tinkham, Chapter 3 (BCS theory) for the mathematical details we omitted. Laughlin's Nobel lecture is a gem of scientific writing.

  5. If the quantum Hall effect fascinates you: Read Girvin's lecture notes (arXiv: cond-mat/9907002). They are the best pedagogical introduction to the QHE at any level.

  6. If you want to connect to Chapter 36 (topology): Read Bernevig, Chapters 1-5, which build directly on the tight-binding models of this chapter.