Quantum Hall Effect and Composite Particles
This chapter discusses a brief introduction to the quantum Hall effect (QHE). It explores the classical Hall effect and then study the quantum Hall effect by solving the Landau level problem in quantum mechanics. The chapter introduces the Laughlin wavefunction as a many-body wave-function which leads, through the plasma analogy, to fractional fillings and thus a solution of the fractional QHE problem. It focuses on the idea of localisation leading to plateau formation. The chapter describes a Chern-Simons theory of the QHE and also introduces Jain’s composite fermions. To understand Integer quantum Hall effect let begin by considering the Landau Level problem in quantum mechanics of a charged particle in 2D moving in a perpendicular magnetic field. The problem of electrons moving in a magnetic field in 2D in the absence of disorder leads to the picture of highly degenerate Landau levels which are seperated in energy by gaps of cyclotron energy ℏω.