Energy Gaps in Fractional Quantum Hall States

Sasaki, Shosuke

doi:https://doi.org/10.1088/1742-6596/100/4/042021

Energy Gaps in Fractional Quantum Hall States

Sasaki, Shosuke

Journal of Physics: Conference Series, 2008, 100(4), 42021

アクセス数:292件（2025-07-06 12:57 集計）

固定URL: https://hdl.handle.net/11094/27138

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タイトル	Energy Gaps in Fractional Quantum Hall States
著者	NRID 1000060029717 1000060029717 著者名 Sasaki, Shosuke
内容	IVC-17/ICSS-13 and ICN+T2007
抄録	Energy values versus filling factors v are examined for fractional quantum Hall states (FQHS). First, the classical Coulomb energy of nearest electron pairs in FQHS is shown to be linearly dependent upon 1/v. The residual Coulomb interaction produces quantum transitions. Examination of second order transitions indicates a discrepancy between the second order perturbation energy at v = 2/3 and the limiting energy value at v = (2s + 1)/(3s + 1) for an infinitely large value of s. Accordingly, an energy gap appears at v = 2/3. On the other hand, the second order perturbation energy epsilon2(v = 3/4) is equal to the limiting energy value at v = (3s + 1)/(4s + 1) for an infinitely large s. Therefore, the energy spectrum is continuous near v = 3/4, meaning that it is gapless at v = 3/4. The same mechanisms appear in higher order perturbation calculations because the number of forbidden transitions in the higher order calculation is equal to that in the second order calculation. That is to say, the gap and gapless mechanisms can be extended to higher order calculations. In fractional filling factors other than v = 2/3 and 3/4, either a gap mechanism or a gapless mechanism appears for each filling factor. Consequently, our results can theoretically explain the precise confinement of Hall resistance at fractional filling factors with a gap mechanism.
出版者	IOP Publishing
収録物名	Journal of Physics: Conference Series
巻(号)	100(4)
ページ	42021
刊行年月	2008
言語	英語
ハンドルURL	https://hdl.handle.net/11094/27138
PISSN	17426588
関連情報 (isIdenticalTo)	DOI (出版社版) https://doi.org/10.1088/1742-6596/100/4/042021
アクセス権	open access
権利情報	Published under licence in Journal of Physics: Conference Series by IOP Publishing Ltd. CC-BY Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
権利情報	http://creativecommons.org/licenses/by/3.0/
出版タイプ	Version of Record
カテゴリ	学術雑誌論文 Journal Article

資源タイプ	学術雑誌論文
ローカル資源タイプ	学術雑誌論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Journal of Physics: Conference Series. 2008, 100(4), p. 42021
DC.title	Energy Gaps in Fractional Quantum Hall States
DC.creator	Sasaki, Shosuke
DC.publisher	IOP Publishing
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2008
DC.identifier	https://doi.org/10.1088/1742-6596/100/4/042021
DC.description	IVC-17/ICSS-13 and ICN+T2007
DCTERMS.abstract	Energy values versus filling factors v are examined for fractional quantum Hall states (FQHS). First, the classical Coulomb energy of nearest electron pairs in FQHS is shown to be linearly dependent upon 1/v. The residual Coulomb interaction produces quantum transitions. Examination of second order transitions indicates a discrepancy between the second order perturbation energy at v = 2/3 and the limiting energy value at v = (2s + 1)/(3s + 1) for an infinitely large value of s. Accordingly, an energy gap appears at v = 2/3. On the other hand, the second order perturbation energy epsilon2(v = 3/4) is equal to the limiting energy value at v = (3s + 1)/(4s + 1) for an infinitely large s. Therefore, the energy spectrum is continuous near v = 3/4, meaning that it is gapless at v = 3/4. The same mechanisms appear in higher order perturbation calculations because the number of forbidden transitions in the higher order calculation is equal to that in the second order calculation. That is to say, the gap and gapless mechanisms can be extended to higher order calculations. In fractional filling factors other than v = 2/3 and 3/4, either a gap mechanism or a gapless mechanism appears for each filling factor. Consequently, our results can theoretically explain the precise confinement of Hall resistance at fractional filling factors with a gap mechanism.
DC.rights	Published under licence in Journal of Physics: Conference Series by IOP Publishing Ltd. CC-BY Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
DC.rights	http://creativecommons.org/licenses/by/3.0/
DC.format	27138
citation_title	Energy Gaps in Fractional Quantum Hall States
citation_author	Sasaki, Shosuke
citation_publisher	IOP Publishing
citation_language	英語
citation_date	2008
citation_journal_title	Journal of Physics: Conference Series
citation_volume	100
citation_issue	4
citation_firstpage	42021
citation_doi	https://doi.org/10.1088/1742-6596/100/4/042021
citation_public_url	https://hdl.handle.net/11094/27138

Energy Gaps in Fractional Quantum Hall States

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