Topological invariants in two-dimensional quasicrystals
We provide a topological concept to characterize energy gaps in general two-dimensional quasiperiodic systems. We show that every single gap is uniquely characterized by a set of integers, which quantize the area of the momentum space in units of multiple Brillouin zones. These integers are found to...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2022-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.013028 |
| _version_ | 1827285609436151808 |
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| author | Mikito Koshino Hiroki Oka |
| author_facet | Mikito Koshino Hiroki Oka |
| author_sort | Mikito Koshino |
| collection | DOAJ |
| description | We provide a topological concept to characterize energy gaps in general two-dimensional quasiperiodic systems. We show that every single gap is uniquely characterized by a set of integers, which quantize the area of the momentum space in units of multiple Brillouin zones. These integers are found to be equivalent to the second Chern numbers by considering a formal relationship between an adiabatic charge pumping under a potential sliding and the four-dimensional quantum Hall effect. The integers are independent of commensurability, and invariant under an arbitrary continuous deformation, such as a relative rotation of a twisted bilayer system. |
| first_indexed | 2024-04-24T10:17:40Z |
| format | Article |
| id | doaj.art-c0998b48587b4dc58fc001e416ea7e48 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:17:40Z |
| publishDate | 2022-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-c0998b48587b4dc58fc001e416ea7e482024-04-12T17:17:07ZengAmerican Physical SocietyPhysical Review Research2643-15642022-01-014101302810.1103/PhysRevResearch.4.013028Topological invariants in two-dimensional quasicrystalsMikito KoshinoHiroki OkaWe provide a topological concept to characterize energy gaps in general two-dimensional quasiperiodic systems. We show that every single gap is uniquely characterized by a set of integers, which quantize the area of the momentum space in units of multiple Brillouin zones. These integers are found to be equivalent to the second Chern numbers by considering a formal relationship between an adiabatic charge pumping under a potential sliding and the four-dimensional quantum Hall effect. The integers are independent of commensurability, and invariant under an arbitrary continuous deformation, such as a relative rotation of a twisted bilayer system.http://doi.org/10.1103/PhysRevResearch.4.013028 |
| spellingShingle | Mikito Koshino Hiroki Oka Topological invariants in two-dimensional quasicrystals Physical Review Research |
| title | Topological invariants in two-dimensional quasicrystals |
| title_full | Topological invariants in two-dimensional quasicrystals |
| title_fullStr | Topological invariants in two-dimensional quasicrystals |
| title_full_unstemmed | Topological invariants in two-dimensional quasicrystals |
| title_short | Topological invariants in two-dimensional quasicrystals |
| title_sort | topological invariants in two dimensional quasicrystals |
| url | http://doi.org/10.1103/PhysRevResearch.4.013028 |
| work_keys_str_mv | AT mikitokoshino topologicalinvariantsintwodimensionalquasicrystals AT hirokioka topologicalinvariantsintwodimensionalquasicrystals |