The Quantum Hall Effect

The quantum Hall effects remains one of the most important subjects to have emerged in condensed matter physics over the past 20 years. The fractional quantum Hall effect, in particular, has opened up a new paradigm in the study of strongly correlated electrons, and it has been shown that new concepts, such as fractional statistics, anyon, chiral Luttinger liquid and composite particles, are realized in two-dimensional electron systems. This book explains the quantum Hall effects together with these new concepts starting from elementary quantum mechanics. Thus, graduate students can use this book to gain an overall understanding of these phenomena.

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Today, more than 20 years after the discovery of the quantum Hall effect, the number of publications in this field, at more than one paper per day, is still increasing. This remarkable fact requires some explanation. It also poses, but perhaps also answers, the question of why a new monograph entitled 'The Quantum Hall Effect' is a highly desirable addition to the literature. Originally the quantum Hall effect (QHE) was a term coined to describe the unexpected observation of a fundamental electrical resistance, with a value independent of the microscopic details of the semiconductor device. The simplest explanation of this phenomenon was based on an independent electron picture. The subsequent discovery of the fractional quantum Hall ef fect demonstrated that a many-body wave function and a more global view of the system is necessary to incorporate and explain interesting new aspects. Today, the quantum Hall effect has become a pseudonym for many differ ent phenomena observed in high magnetic fields, with connections not only to solid state physics but also to theoretical descriptions in plasma physics, astrophysics, atomic physics, and high energy physics. There are even spec ulations that a higher-dimensional generalization of the QHE may be useful for discussing questions related to the basic properties of space.