The Quantum Hall Effect: Poincaré Seminar (Progress in Mathematical Physics)

Abstract

The Séminaire Poincaré provides hopefully accessible, accurate and up-to-date reviews of important topics in physics. The seminar usually invites people from both experiment and theory to discuss aspects of the topic. Recent topics, including Entropy (2003), Einstein (2005), and Quantum Decoherence (2005), demonstrate a determination on the part of the organisers to keep the seminar attractive to almost anyone active in physics and to avoid becoming too focused on a specialist area of research. A seminar on the quantum hall effect (QHE) was held in 2004. There were presentations by Klaus von Klitzing (Historical overview), Benoit Doucot and Vincent Pasquier (Introductory Theory), Blaise Jeanneret and Beat Jeckelman (QHE as an electrical resistance standard), Steven Girvin (Introduction to the Fractional QHE) and by Christian Glattli (Tunneling in the FQHE regime). This book is the collection of their contributions. The QHE as a field is already well-served by a small number of excellent books containing original articles by collections of authors and by a reprint volume, so it was not at all clear what a new volume could contribute. Well, this seminar has found something. It concentrates on experimental aspects not so often reviewed and keeps the theory as non-technical as possible. The introductory notes on the theory of electrons in a strong magnetic field give a beautiful explanation of the background theory. In the rush to get onto the technically challenging theory, this material is often assumed part of everyone's background knowledge or it is oversimplified. At the level of a first year graduate student/final year masters student, the chapter takes the reader carefully through projection onto a Landau level, Laughlin's original argument for the quantization of the Hall effect and the link to a topological invariant. Steve Girvin's chapter is at approximately the same level. It covers introductory material on the Laughlin wavefunction and its neutral and charge excitations. The chapter on metrology is a stand-alone article about the use of the QHE in defining absolute standards of measurement. The authors have given an interesting account of how the small deviations from an absolute standard or resistance depend on aspects of the samples, the current distribution, the temperature, edge states as well as contacts. They also explain how the QHE is now used by most metrology institutes to provide a dc reference for the Ohm. The final chapter on tunneling in FQHE systems looks at conductance and shot noise measurements (many of which were made by collaborations including the author). Backscattering in the FQHE by constrictions lead to a non-linear conductance in which the exponent varies as a power of voltage, which (according to theory) is quantized, and in which the shot noise directly measures the charge of the elementary excitation. This chapter is very welcome. It manages to explain what is actually measured and how to think about the implications without including technical theory.