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Topological Classification of Correlations in 2D Electron Systems in Magnetic or Berry Fields

Recent topology classification of 2D electron states induced by different homotopy classes of mappings of the planar Brillouin zone into Bloch space can be supplemented by a homotopy classification of various phases of multi-electron homotopy patterns induced by Coulomb interaction between electrons...

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Autor principal: Jacak, Janusz E.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8037989/
https://www.ncbi.nlm.nih.gov/pubmed/33801698
http://dx.doi.org/10.3390/ma14071650
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author Jacak, Janusz E.
author_facet Jacak, Janusz E.
author_sort Jacak, Janusz E.
collection PubMed
description Recent topology classification of 2D electron states induced by different homotopy classes of mappings of the planar Brillouin zone into Bloch space can be supplemented by a homotopy classification of various phases of multi-electron homotopy patterns induced by Coulomb interaction between electrons. The general classification of such type is presented. It explains the topologically protected correlations responsible for integer and fractional Hall effects in 2D multi-electron systems in the presence of perpendicular quantizing magnetic field or Berry field, the latter in topological Chern insulators. The long-range quantum entanglement is essential for homotopy correlated phases in contrast to local binary entanglement for conventional phases with local order parameters. The classification of homotopy long-range correlated phases induced by the Coulomb interaction of electrons has been derived in terms of homotopy invariants and illustrated by experimental observations in GaAs 2DES, graphene monolayer, and bilayer and in Chern topological insulators. The homotopy phases are demonstrated to be topologically protected and immune to the local crystal field, local disorder, and variation of the electron interaction strength. The nonzero interaction between electrons is shown, however, to be essential for the definition of the homotopy invariants, which disappear in gaseous systems.
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spelling pubmed-80379892021-04-12 Topological Classification of Correlations in 2D Electron Systems in Magnetic or Berry Fields Jacak, Janusz E. Materials (Basel) Article Recent topology classification of 2D electron states induced by different homotopy classes of mappings of the planar Brillouin zone into Bloch space can be supplemented by a homotopy classification of various phases of multi-electron homotopy patterns induced by Coulomb interaction between electrons. The general classification of such type is presented. It explains the topologically protected correlations responsible for integer and fractional Hall effects in 2D multi-electron systems in the presence of perpendicular quantizing magnetic field or Berry field, the latter in topological Chern insulators. The long-range quantum entanglement is essential for homotopy correlated phases in contrast to local binary entanglement for conventional phases with local order parameters. The classification of homotopy long-range correlated phases induced by the Coulomb interaction of electrons has been derived in terms of homotopy invariants and illustrated by experimental observations in GaAs 2DES, graphene monolayer, and bilayer and in Chern topological insulators. The homotopy phases are demonstrated to be topologically protected and immune to the local crystal field, local disorder, and variation of the electron interaction strength. The nonzero interaction between electrons is shown, however, to be essential for the definition of the homotopy invariants, which disappear in gaseous systems. MDPI 2021-03-27 /pmc/articles/PMC8037989/ /pubmed/33801698 http://dx.doi.org/10.3390/ma14071650 Text en © 2021 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) ).
spellingShingle Article
Jacak, Janusz E.
Topological Classification of Correlations in 2D Electron Systems in Magnetic or Berry Fields
title Topological Classification of Correlations in 2D Electron Systems in Magnetic or Berry Fields
title_full Topological Classification of Correlations in 2D Electron Systems in Magnetic or Berry Fields
title_fullStr Topological Classification of Correlations in 2D Electron Systems in Magnetic or Berry Fields
title_full_unstemmed Topological Classification of Correlations in 2D Electron Systems in Magnetic or Berry Fields
title_short Topological Classification of Correlations in 2D Electron Systems in Magnetic or Berry Fields
title_sort topological classification of correlations in 2d electron systems in magnetic or berry fields
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8037989/
https://www.ncbi.nlm.nih.gov/pubmed/33801698
http://dx.doi.org/10.3390/ma14071650
work_keys_str_mv AT jacakjanusze topologicalclassificationofcorrelationsin2delectronsystemsinmagneticorberryfields