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.
- 1. The Basics:
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:
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:
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:
Higher Landau Levels. The Moore-Read Pfaffian State, Majorana Zero Modes, Read-Rezayi States. Non-Abelian Anyons, fusion and braiding.
- 5. Chern-Simons Theories:
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:
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
- The Quantum Hall Effect by Steven Girvin
- Quantum Hall Effects by Mark Goerbig
- Topological Quantum Numbers in Condensed Matter Systems by Sebastian Huber
- Three Lectures on Topological Phases of Matter by Edward Witten
- Aspects of Chern-Simons Theory by Gerald Dunne
- Quantum Condensed Matter Physics by Chetan Nayak