Topological edge states in two-gap unitary systems: a transfer matrix approach
We construct and investigate a family of two-band unitary systems living on a cylinder geometry and presenting localized edge states. Using the transfer matrix formalism, we solve and investigate in detail such states in the thermodynamic limit. Analytic considerations then suggest the construction...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2015-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/17/11/115008 |
| _version_ | 1797751059745079296 |
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| author | Clément Tauber Pierre Delplace |
| author_facet | Clément Tauber Pierre Delplace |
| author_sort | Clément Tauber |
| collection | DOAJ |
| description | We construct and investigate a family of two-band unitary systems living on a cylinder geometry and presenting localized edge states. Using the transfer matrix formalism, we solve and investigate in detail such states in the thermodynamic limit. Analytic considerations then suggest the construction of a family of Riemann surfaces associated to the band structure of the system. In this picture, the corresponding edge states naturally wind around non-contractile loops, defining a topological invariant associated to each gap of the system. |
| first_indexed | 2024-03-12T16:42:58Z |
| format | Article |
| id | doaj.art-dd07c5720ade416c91a0539412b05cf4 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:42:58Z |
| publishDate | 2015-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-dd07c5720ade416c91a0539412b05cf42023-08-08T14:24:00ZengIOP PublishingNew Journal of Physics1367-26302015-01-01171111500810.1088/1367-2630/17/11/115008Topological edge states in two-gap unitary systems: a transfer matrix approachClément Tauber0Pierre Delplace1Laboratoire de Physique de l’École Normale Supérieure de Lyon, UMR CNRS 5672, 46 allée d’Italie, F-69364 LYON CEDEX 07, FranceLaboratoire de Physique de l’École Normale Supérieure de Lyon, UMR CNRS 5672, 46 allée d’Italie, F-69364 LYON CEDEX 07, FranceWe construct and investigate a family of two-band unitary systems living on a cylinder geometry and presenting localized edge states. Using the transfer matrix formalism, we solve and investigate in detail such states in the thermodynamic limit. Analytic considerations then suggest the construction of a family of Riemann surfaces associated to the band structure of the system. In this picture, the corresponding edge states naturally wind around non-contractile loops, defining a topological invariant associated to each gap of the system.https://doi.org/10.1088/1367-2630/17/11/115008Harper modeltransfer matrix methodRiemann surfacesFloquet systemschiral edge statesphotonic lattices |
| spellingShingle | Clément Tauber Pierre Delplace Topological edge states in two-gap unitary systems: a transfer matrix approach New Journal of Physics Harper model transfer matrix method Riemann surfaces Floquet systems chiral edge states photonic lattices |
| title | Topological edge states in two-gap unitary systems: a transfer matrix approach |
| title_full | Topological edge states in two-gap unitary systems: a transfer matrix approach |
| title_fullStr | Topological edge states in two-gap unitary systems: a transfer matrix approach |
| title_full_unstemmed | Topological edge states in two-gap unitary systems: a transfer matrix approach |
| title_short | Topological edge states in two-gap unitary systems: a transfer matrix approach |
| title_sort | topological edge states in two gap unitary systems a transfer matrix approach |
| topic | Harper model transfer matrix method Riemann surfaces Floquet systems chiral edge states photonic lattices |
| url | https://doi.org/10.1088/1367-2630/17/11/115008 |
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