A $C^\ast$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals
Understanding the interaction of real- and reciprocal space topology in skyrmion crystals is an open problem. We approach it from the viewpoint of $C^\ast$-algebras and calculate all admissible Chern numbers of a strongly coupled tight-binding skyrmion system on a triangular lattice as a function of...
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| Format: | Article |
| Language: | English |
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SciPost
2024-12-01
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| Series: | SciPost Physics Core |
| Online Access: | https://scipost.org/SciPostPhysCore.7.4.080 |
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| author | Pascal Prass, Fabian R. Lux, Emil Prodan, Duco van Straten, Yuriy Mokrousov |
| author_facet | Pascal Prass, Fabian R. Lux, Emil Prodan, Duco van Straten, Yuriy Mokrousov |
| author_sort | Pascal Prass, Fabian R. Lux, Emil Prodan, Duco van Straten, Yuriy Mokrousov |
| collection | DOAJ |
| description | Understanding the interaction of real- and reciprocal space topology in skyrmion crystals is an open problem. We approach it from the viewpoint of $C^\ast$-algebras and calculate all admissible Chern numbers of a strongly coupled tight-binding skyrmion system on a triangular lattice as a function of Fermi energy and texture parameters. Our analysis reveals the topological complexity of electronic states coupled to spin textures, and the failure of the adiabatic picture to account for it in terms of emergent electromagnetism. On the contrary, we explain the discontinuous jumps in the real-space winding number in terms of collective evolution in real-, reciprocal, and mixed space Chern numbers. Our work sets the stage for further research on topological dynamics in complex dynamic spin textures coupled to external fields. |
| format | Article |
| id | doaj-art-a7d9ebdcac2a4b5995211ed6c59e2ce1 |
| institution | OA Journals |
| issn | 2666-9366 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics Core |
| spelling | doaj-art-a7d9ebdcac2a4b5995211ed6c59e2ce12025-08-20T02:35:54ZengSciPostSciPost Physics Core2666-93662024-12-017408010.21468/SciPostPhysCore.7.4.080A $C^\ast$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystalsPascal Prass, Fabian R. Lux, Emil Prodan, Duco van Straten, Yuriy MokrousovUnderstanding the interaction of real- and reciprocal space topology in skyrmion crystals is an open problem. We approach it from the viewpoint of $C^\ast$-algebras and calculate all admissible Chern numbers of a strongly coupled tight-binding skyrmion system on a triangular lattice as a function of Fermi energy and texture parameters. Our analysis reveals the topological complexity of electronic states coupled to spin textures, and the failure of the adiabatic picture to account for it in terms of emergent electromagnetism. On the contrary, we explain the discontinuous jumps in the real-space winding number in terms of collective evolution in real-, reciprocal, and mixed space Chern numbers. Our work sets the stage for further research on topological dynamics in complex dynamic spin textures coupled to external fields.https://scipost.org/SciPostPhysCore.7.4.080 |
| spellingShingle | Pascal Prass, Fabian R. Lux, Emil Prodan, Duco van Straten, Yuriy Mokrousov A $C^\ast$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals SciPost Physics Core |
| title | A $C^\ast$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals |
| title_full | A $C^\ast$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals |
| title_fullStr | A $C^\ast$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals |
| title_full_unstemmed | A $C^\ast$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals |
| title_short | A $C^\ast$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals |
| title_sort | c ast algebraic view on the interaction of real and reciprocal space topology in skyrmion crystals |
| url | https://scipost.org/SciPostPhysCore.7.4.080 |
| work_keys_str_mv | AT pascalprassfabianrluxemilprodanducovanstratenyuriymokrousov acastalgebraicviewontheinteractionofrealandreciprocalspacetopologyinskyrmioncrystals AT pascalprassfabianrluxemilprodanducovanstratenyuriymokrousov castalgebraicviewontheinteractionofrealandreciprocalspacetopologyinskyrmioncrystals |