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 and are also avaiable to download from the arXiv.

Full Lecture Notes

Individual Chapters

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

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.

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.

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.

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.

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

Videos

I gave these lectures at the Tata Institute of Fundamental Research in Mumbai, India. The first lecture, on Landau levels, wasn't recorded but the others can be viewed below.