David Tong: The Quantum Hall Effect

David Tong: Lectures on the Quantum Hall Effect

This is a course on the quantum Hall effect, given in TIFR, Mumbai. The first four chapters require only basic quantum mechanics; the final two chapters need techniques from quantum field theory. The full lecture notes are around 230 pages. They are also available to download at the arXiv. Please do email me if you find any typos or mistakes.


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Content


  • 1. The Basics:   PDF
    The classical Hall effect, the integer quantum Hall effect and the fractional quantum Hall effect. Landau levels, Landau gauge and symmetric gauge. Berry phase, Aharonov-Bohm effect, Non-Abelian Berry Holonomy

  • 2. The Integer Quantum Hall Effect:   PDF
    Conductivity and Edge Modes. Disorder and Gauge Invariance. The Kubo formula. Topology, TKNN Invariants and the Chern Insulator. The Hofstadter Butterfly.

  • 3. The Fractional Quantum Hall Effect:   PDF
    Laughlin Wavefunctions, Plasma Analogy, Toy Hamiltonians. Quasi-Holes and Quasi-Particles. Anyons, Fractional Charge and Fractional Statistics. Topological Order. Quantum Hall Hierarchy and Composite Fermions. The Half-Filled Landau level.

  • 4. Non-Abelian Quantum Hall States:   PDF
    Higher Landau Levels. The Moore-Read Pfaffian State, Majorana Zero Modes, Read-Rezayi States. Non-Abelian Anyons, fusion and braiding.

  • 5. Chern-Simons Theories:   PDF
    Chern-Simons terms for the Integer Quantum Hall Effect, Quantisation of Chern-Simons Level; Chern-Simons Theory for the Fractional Quantum Hall Effect, K-Matrices; Particle-Vortex Duality, Chern-Simons Ginzburg-Landau Theory; Non-Abelian Chern-Simons Theory, Canonical Quantisation, Wilson Lines.

  • 6. Edge Modes:   PDF
    Edge Modes for Laughlin States, The Chiral Boson, Tunnelling; The Bulk/Boundary Correspondence; The Free Fermion and the Moore-Read State; Conformal Field Theory


Quantum Hall Effect on the Web


A Summary of the Lectures in Pretty Pictures