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 |
| Summary: | 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. |
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| ISSN: | 2542-4653 |