Euler band topology in spin-orbit coupled magnetic systems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910422977740800 |
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| author | Lee, Seung Hun Qian, Yuting Yang, Bohm-Jung |
| author_facet | Lee, Seung Hun Qian, Yuting Yang, Bohm-Jung |
| contents | The Euler class characterizes the topology of two real bands isolated from other bands in two-dimensions. Despite various intriguing topological properties predicted up to now, the candidate real materials hosting electronic Euler bands are extremely rare. Here, we show that in a quantum spin Hall insulator with two-fold rotation $C_{2z}$ about the $z$-axis, a pair of bands with nontrivial $\mathbb{Z}_2$ invariant turn into magnetic Euler bands under in-plane Zeeman field or in-plane ferromagnetic ordering. The resulting magnetic insulator generally carries a nontrivial second Stiefel-Whitney invariant. In particular, when the topmost pair of occupied bands carry a nonzero Euler number, the corresponding magnetic insulator can be called a magnetic Euler insulator. Moreover, the topological phase transition between a trivial magnetic insulator and a magnetic Stiefel-Whitney or Euler insulator is mediated by a stable topological semimetal phase in which Dirac nodes carrying non-Abelian topological charges exhibit braiding processes across the transition. Using the first-principles calculations, we propose various candidate materials hosting magnetic Euler bands. We especially show that ZrTe$_5$ bilayers under in-plane ferromagnetism are a candidate system for magnetic Stiefel-Whitney insulators in which the non-Abelian braiding-induced topological phase transitions can occur under pressure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16383 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Euler band topology in spin-orbit coupled magnetic systems Lee, Seung Hun Qian, Yuting Yang, Bohm-Jung Mesoscale and Nanoscale Physics The Euler class characterizes the topology of two real bands isolated from other bands in two-dimensions. Despite various intriguing topological properties predicted up to now, the candidate real materials hosting electronic Euler bands are extremely rare. Here, we show that in a quantum spin Hall insulator with two-fold rotation $C_{2z}$ about the $z$-axis, a pair of bands with nontrivial $\mathbb{Z}_2$ invariant turn into magnetic Euler bands under in-plane Zeeman field or in-plane ferromagnetic ordering. The resulting magnetic insulator generally carries a nontrivial second Stiefel-Whitney invariant. In particular, when the topmost pair of occupied bands carry a nonzero Euler number, the corresponding magnetic insulator can be called a magnetic Euler insulator. Moreover, the topological phase transition between a trivial magnetic insulator and a magnetic Stiefel-Whitney or Euler insulator is mediated by a stable topological semimetal phase in which Dirac nodes carrying non-Abelian topological charges exhibit braiding processes across the transition. Using the first-principles calculations, we propose various candidate materials hosting magnetic Euler bands. We especially show that ZrTe$_5$ bilayers under in-plane ferromagnetism are a candidate system for magnetic Stiefel-Whitney insulators in which the non-Abelian braiding-induced topological phase transitions can occur under pressure. |
| title | Euler band topology in spin-orbit coupled magnetic systems |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2404.16383 |