Quantized Berry winding from an emergent $\mathcal{PT}$ symmetry
Linear crossings of energy bands occur in a wide variety of materials. In this paper we address the question of the quantization of the Berry winding characterizing the topology of these crossings in dimension $D=2$. Based on the historical example of $2$-bands crossing occuring in graphene, we prop...
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| Format: | Article |
| Language: | English |
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SciPost
2023-10-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.15.4.129 |
| _version_ | 1797667754905436160 |
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| author | Thibaud Louvet, Pierre Delplace, Mark-Oliver Goerbig, David Carpentier |
| author_facet | Thibaud Louvet, Pierre Delplace, Mark-Oliver Goerbig, David Carpentier |
| author_sort | Thibaud Louvet, Pierre Delplace, Mark-Oliver Goerbig, David Carpentier |
| collection | DOAJ |
| description | Linear crossings of energy bands occur in a wide variety of materials. In this paper we address the question of the quantization of the Berry winding characterizing the topology of these crossings in dimension $D=2$. Based on the historical example of $2$-bands crossing occuring in graphene, we propose to relate these Berry windings to the topological Chern number within a $D=3$ dimensional extension of these crossings. This dimensional embedding is obtained through a choice of a gap-opening potential. We show that the presence of an (emergent) $\mathcal{PT}$ symmetry, local in momentum and antiunitary, allows the quantization of the Berry windings as multiples of $\pi$. We illustrate this quantization mechanism on a variety of three-band crossings. |
| first_indexed | 2024-03-11T20:17:57Z |
| format | Article |
| id | doaj.art-19ba5617ed6547c1a3d98aeb24b6cd33 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-03-11T20:17:57Z |
| publishDate | 2023-10-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-19ba5617ed6547c1a3d98aeb24b6cd332023-10-03T09:52:22ZengSciPostSciPost Physics2542-46532023-10-0115412910.21468/SciPostPhys.15.4.129Quantized Berry winding from an emergent $\mathcal{PT}$ symmetryThibaud Louvet, Pierre Delplace, Mark-Oliver Goerbig, David CarpentierLinear crossings of energy bands occur in a wide variety of materials. In this paper we address the question of the quantization of the Berry winding characterizing the topology of these crossings in dimension $D=2$. Based on the historical example of $2$-bands crossing occuring in graphene, we propose to relate these Berry windings to the topological Chern number within a $D=3$ dimensional extension of these crossings. This dimensional embedding is obtained through a choice of a gap-opening potential. We show that the presence of an (emergent) $\mathcal{PT}$ symmetry, local in momentum and antiunitary, allows the quantization of the Berry windings as multiples of $\pi$. We illustrate this quantization mechanism on a variety of three-band crossings.https://scipost.org/SciPostPhys.15.4.129 |
| spellingShingle | Thibaud Louvet, Pierre Delplace, Mark-Oliver Goerbig, David Carpentier Quantized Berry winding from an emergent $\mathcal{PT}$ symmetry SciPost Physics |
| title | Quantized Berry winding from an emergent $\mathcal{PT}$ symmetry |
| title_full | Quantized Berry winding from an emergent $\mathcal{PT}$ symmetry |
| title_fullStr | Quantized Berry winding from an emergent $\mathcal{PT}$ symmetry |
| title_full_unstemmed | Quantized Berry winding from an emergent $\mathcal{PT}$ symmetry |
| title_short | Quantized Berry winding from an emergent $\mathcal{PT}$ symmetry |
| title_sort | quantized berry winding from an emergent mathcal pt symmetry |
| url | https://scipost.org/SciPostPhys.15.4.129 |
| work_keys_str_mv | AT thibaudlouvetpierredelplacemarkolivergoerbigdavidcarpentier quantizedberrywindingfromanemergentmathcalptsymmetry |