A note contrasting two microscopic theories of the fractional quantum Hall effect

Jainendra K. Jain

doi:10.1007/s12648-014-0491-9

A note contrasting two microscopic theories of the fractional quantum Hall effect

Jainendra K. Jain

Research output: Contribution to journal › Article › peer-review

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Abstract

Two microscopic theories have been proposed for the explanation of the fractional quantum Hall effect, namely the Haldane-Halperin hierarchy theory and the composite fermion theory. Contradictory statements have been made regarding the relation between them, ranging from their being distinct to their being completely equivalent. This article attempts to provide a clarification of the issue. It is shown that the two theories postulate distinct microscopic mechanisms for the origin of the fractional quantum Hall effect, and make substantially different predictions that have allowed experiments to distinguish between them.

Original language	English (US)
Pages (from-to)	915-929
Number of pages	15
Journal	Indian Journal of Physics
Volume	88
Issue number	9
DOIs	https://doi.org/10.1007/s12648-014-0491-9
State	Published - Sep 2014

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1007/s12648-014-0491-9

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title = "A note contrasting two microscopic theories of the fractional quantum Hall effect",

abstract = "Two microscopic theories have been proposed for the explanation of the fractional quantum Hall effect, namely the Haldane-Halperin hierarchy theory and the composite fermion theory. Contradictory statements have been made regarding the relation between them, ranging from their being distinct to their being completely equivalent. This article attempts to provide a clarification of the issue. It is shown that the two theories postulate distinct microscopic mechanisms for the origin of the fractional quantum Hall effect, and make substantially different predictions that have allowed experiments to distinguish between them.",

author = "Jain, {Jainendra K.}",

note = "Funding Information: Acknowledgments I am grateful to H. L. Stormer for permission to use Fig. 3 and for the list of observed fractions given in Fig. 4. I am indebted to B. I. Halperin for detailed and insightful comments on an earlier version of this manuscript, which have been incorporated into the article, and for his kind encouragement. I also thank J. R. Banavar, S. Das Sarma, G. Murthy, D. S. Weiss, A. W{\'o}js, and Y.-H. Wu for useful discussions in this context. Financial support from DOE under Grant No. DE-SC0005042 is gratefully acknowledged.",

year = "2014",

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doi = "10.1007/s12648-014-0491-9",

language = "English (US)",

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N1 - Funding Information: Acknowledgments I am grateful to H. L. Stormer for permission to use Fig. 3 and for the list of observed fractions given in Fig. 4. I am indebted to B. I. Halperin for detailed and insightful comments on an earlier version of this manuscript, which have been incorporated into the article, and for his kind encouragement. I also thank J. R. Banavar, S. Das Sarma, G. Murthy, D. S. Weiss, A. Wójs, and Y.-H. Wu for useful discussions in this context. Financial support from DOE under Grant No. DE-SC0005042 is gratefully acknowledged.

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N2 - Two microscopic theories have been proposed for the explanation of the fractional quantum Hall effect, namely the Haldane-Halperin hierarchy theory and the composite fermion theory. Contradictory statements have been made regarding the relation between them, ranging from their being distinct to their being completely equivalent. This article attempts to provide a clarification of the issue. It is shown that the two theories postulate distinct microscopic mechanisms for the origin of the fractional quantum Hall effect, and make substantially different predictions that have allowed experiments to distinguish between them.

AB - Two microscopic theories have been proposed for the explanation of the fractional quantum Hall effect, namely the Haldane-Halperin hierarchy theory and the composite fermion theory. Contradictory statements have been made regarding the relation between them, ranging from their being distinct to their being completely equivalent. This article attempts to provide a clarification of the issue. It is shown that the two theories postulate distinct microscopic mechanisms for the origin of the fractional quantum Hall effect, and make substantially different predictions that have allowed experiments to distinguish between them.

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JF - Indian Journal of Physics

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A note contrasting two microscopic theories of the fractional quantum Hall effect

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