Partial spectral flow and the Aharonov–Bohm effect in graphene
Abstract We study the Aharonov–Bohm effect in an open-ended tube made of a graphene sheet whose dimensions are much larger than the interatomic distance in graphene. An external magnetic field vanishes on and in the vicinity of the graphene sheet and its flux through the tube is adiabatically switch...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-09-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-020-08464-z |
| _version_ | 1819009896011530240 |
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| author | Mikhail I. Katsnelson Vladimir Nazaikinskii |
| author_facet | Mikhail I. Katsnelson Vladimir Nazaikinskii |
| author_sort | Mikhail I. Katsnelson |
| collection | DOAJ |
| description | Abstract We study the Aharonov–Bohm effect in an open-ended tube made of a graphene sheet whose dimensions are much larger than the interatomic distance in graphene. An external magnetic field vanishes on and in the vicinity of the graphene sheet and its flux through the tube is adiabatically switched on. It is shown that, in the process, the energy levels of the tight-binding Hamiltonian of $$\pi $$ π -electrons unavoidably cross the Fermi level, which results in the creation of electron–hole pairs. The number of pairs is proven to be equal to the number of magnetic flux quanta of the external field. The proof is based on the new notion of partial spectral flow, which generalizes the ordinary spectral flow already having well-known applications (such as the Kopnin forces in superconductors and superfluids) in condensed matter physics. |
| first_indexed | 2024-12-21T01:03:39Z |
| format | Article |
| id | doaj.art-595f3e3c45454ef68d1a6ccd66376558 |
| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-12-21T01:03:39Z |
| publishDate | 2020-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-595f3e3c45454ef68d1a6ccd663765582022-12-21T19:21:06ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522020-09-0180911610.1140/epjc/s10052-020-08464-zPartial spectral flow and the Aharonov–Bohm effect in grapheneMikhail I. Katsnelson0Vladimir Nazaikinskii1Institute for Molecules and Materials, Radboud UniversityIshlinsky Institute for Problems in Mechanics RASAbstract We study the Aharonov–Bohm effect in an open-ended tube made of a graphene sheet whose dimensions are much larger than the interatomic distance in graphene. An external magnetic field vanishes on and in the vicinity of the graphene sheet and its flux through the tube is adiabatically switched on. It is shown that, in the process, the energy levels of the tight-binding Hamiltonian of $$\pi $$ π -electrons unavoidably cross the Fermi level, which results in the creation of electron–hole pairs. The number of pairs is proven to be equal to the number of magnetic flux quanta of the external field. The proof is based on the new notion of partial spectral flow, which generalizes the ordinary spectral flow already having well-known applications (such as the Kopnin forces in superconductors and superfluids) in condensed matter physics.http://link.springer.com/article/10.1140/epjc/s10052-020-08464-z |
| spellingShingle | Mikhail I. Katsnelson Vladimir Nazaikinskii Partial spectral flow and the Aharonov–Bohm effect in graphene European Physical Journal C: Particles and Fields |
| title | Partial spectral flow and the Aharonov–Bohm effect in graphene |
| title_full | Partial spectral flow and the Aharonov–Bohm effect in graphene |
| title_fullStr | Partial spectral flow and the Aharonov–Bohm effect in graphene |
| title_full_unstemmed | Partial spectral flow and the Aharonov–Bohm effect in graphene |
| title_short | Partial spectral flow and the Aharonov–Bohm effect in graphene |
| title_sort | partial spectral flow and the aharonov bohm effect in graphene |
| url | http://link.springer.com/article/10.1140/epjc/s10052-020-08464-z |
| work_keys_str_mv | AT mikhailikatsnelson partialspectralflowandtheaharonovbohmeffectingraphene AT vladimirnazaikinskii partialspectralflowandtheaharonovbohmeffectingraphene |