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4 - The quantum Hall effects

Published online by Cambridge University Press:  05 June 2012

David K. Ferry ,
Stephen M. Goodnick  and
Jonathan Bird
David K. Ferry
Affiliation:
Arizona State University
Stephen M. Goodnick
Affiliation:
Arizona State University
Jonathan Bird
Affiliation:
State University of New York, Buffalo
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Summary

The discovery in 1980, by Klaus von Klitzing and his colleagues, of the integer quantum Hall effect (IQHE) may have done more than any other single event to stimulate experimental and theoretical interest in the electrical properties of low-dimensional systems. This phenomenon has now been observed in a variety of different material systems, and is manifest as the appearance of wide and precisely quantized plateaus in the Hall resistance (RH, or Hall resistivity ρxy), which therefore deviates strongly from the linear dependence on magnetic field that is expected classically. It is now understood that this high-magnetic-field phenomenon is associated with the formation of strongly quantized Landau levels in a two-dimensional electron gas (2DEG), under which conditions current flow is carried by ballistic edge states that are the quantum analog of classical skipping orbits (recallSection 2.5). Thus, the quantum Hall effect represents a remarkable manifestation of one-dimensional transport in a macroscopic system.

In this chapter, we begin by discussing the basic phenomenology of the (integer) quantum Hall effect, which, due to the extreme accuracy of its quantization, has now been adopted as an international standard for the definition of the ohm. We present an interpretation of this effect due to Büttiker, which begins from the concepts of the Landauer formula (Section 3.3) and explains the quantization by considering that edge states propagate ballistically, without dissipation, over the entire sample length.

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Chapter
Information
Transport in Nanostructures , pp. 193 - 247
Publisher: Cambridge University Press
Print publication year: 2009

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