Chapter

Quantum Hall effects

Mark O. Goerbig

in Ultracold Gases and Quantum Information

Published in print May 2011 | ISBN: 9780199603657
Published online September 2011 | e-ISBN: 9780191729515 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199603657.003.0006

Series: Lecture Notes of the Les Houches Summer School

Quantum Hall effects

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This chapter yields an introduction to quantum Hall effects both for non-relativistic electrons in conventional two-dimensional electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief historical overview follows a detailed discussion of the kinetic-energy quantisation of non-relativistic and relativistic electrons in a strong magnetic field (section 2). Section 3 is devoted to the transport characteristics of the integer quantum Hall effect, and the basic aspects of the fractional quantum Hall effect are described in section 4. In section 5, several multicomponent quantum Hall systems are briefly discussed, namely the quantum Hall ferromagnetism, bilayer systems and graphene that may be viewed as a four-component system.

Keywords: integral quantum Hall effect; fractional quantum Hall effect; two-dimensional electron systems; graphene; Landau quantisation; fractional charge; anyons; strong electronic correlations

Chapter.  48696 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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