Quantum Hall effect: from the drude conductivity model to the Chern-Simons field description
The goal of this article is to introduce the quantum Hall effect (QHE) from its classical roots to the quantum integer and fractional versions. This is a robust phenomenon with topological nature. Regarding the fractional quantum Hall effect, its phenomenology and the possibility of vortices with fr...
| Main Authors: | , |
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| Format: | Article |
| Language: | Portuguese |
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Sociedade Brasileira de Física
2023-06-01
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| Series: | Revista Brasileira de Ensino de Física |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172023000100435&tlng=en |
| _version_ | 1827909008863789056 |
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| author | G. B. de Gracia B.M. Pimentel |
| author_facet | G. B. de Gracia B.M. Pimentel |
| author_sort | G. B. de Gracia |
| collection | DOAJ |
| description | The goal of this article is to introduce the quantum Hall effect (QHE) from its classical roots to the quantum integer and fractional versions. This is a robust phenomenon with topological nature. Regarding the fractional quantum Hall effect, its phenomenology and the possibility of vortices with fractional charges are also discussed. The lattice structure of graphene, one of the possible planar matter samples in which quantum Hall effects can occur, is also analyzed. The calculation of the Landau levels occurring in this specific substrate is carefully performed. For completeness, a field description for a whole class of these systems, the ones related to the fractional quantum Hall effect, is also reviewed. |
| first_indexed | 2024-03-13T01:31:21Z |
| format | Article |
| id | doaj.art-c45545d678564d629faaad48a5532746 |
| institution | Directory Open Access Journal |
| issn | 1806-9126 |
| language | Portuguese |
| last_indexed | 2024-03-13T01:31:21Z |
| publishDate | 2023-06-01 |
| publisher | Sociedade Brasileira de Física |
| record_format | Article |
| series | Revista Brasileira de Ensino de Física |
| spelling | doaj.art-c45545d678564d629faaad48a55327462023-07-04T07:44:01ZporSociedade Brasileira de FísicaRevista Brasileira de Ensino de Física1806-91262023-06-014510.1590/1806-9126-rbef-2023-0042Quantum Hall effect: from the drude conductivity model to the Chern-Simons field descriptionG. B. de Graciahttps://orcid.org/0000-0003-4303-1846B.M. PimentelThe goal of this article is to introduce the quantum Hall effect (QHE) from its classical roots to the quantum integer and fractional versions. This is a robust phenomenon with topological nature. Regarding the fractional quantum Hall effect, its phenomenology and the possibility of vortices with fractional charges are also discussed. The lattice structure of graphene, one of the possible planar matter samples in which quantum Hall effects can occur, is also analyzed. The calculation of the Landau levels occurring in this specific substrate is carefully performed. For completeness, a field description for a whole class of these systems, the ones related to the fractional quantum Hall effect, is also reviewed.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172023000100435&tlng=enTransport propertiesHall effecttopological |
| spellingShingle | G. B. de Gracia B.M. Pimentel Quantum Hall effect: from the drude conductivity model to the Chern-Simons field description Revista Brasileira de Ensino de Física Transport properties Hall effect topological |
| title | Quantum Hall effect: from the drude conductivity model to the Chern-Simons field description |
| title_full | Quantum Hall effect: from the drude conductivity model to the Chern-Simons field description |
| title_fullStr | Quantum Hall effect: from the drude conductivity model to the Chern-Simons field description |
| title_full_unstemmed | Quantum Hall effect: from the drude conductivity model to the Chern-Simons field description |
| title_short | Quantum Hall effect: from the drude conductivity model to the Chern-Simons field description |
| title_sort | quantum hall effect from the drude conductivity model to the chern simons field description |
| topic | Transport properties Hall effect topological |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172023000100435&tlng=en |
| work_keys_str_mv | AT gbdegracia quantumhalleffectfromthedrudeconductivitymodeltothechernsimonsfielddescription AT bmpimentel quantumhalleffectfromthedrudeconductivitymodeltothechernsimonsfielddescription |