Euler band topology and multiple hinge modes in three-dimensional insulators
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911548093497344 |
|---|---|
| author | Tanaka, Yutaro Kobayashi, Shingo |
| author_facet | Tanaka, Yutaro Kobayashi, Shingo |
| contents | In two-dimensional systems with space-time inversion symmetry, such as $C_{2z}T$, the reality condition on wave functions gives rise to real band topology characterized by the Euler class, a $\mathbb{Z}$-valued topological invariant for a pair of real bands in the Brillouin zone. In this paper, we study three-dimensional $C_{2z}T$-symmetric insulators characterized by $\bar{e}_2$, defined as the difference in the Euler classes between two $C_{2z}T$-invariant planes in the three-dimensional Brillouin zone. By deriving effective surface Hamiltonians from generic low-energy continuum Hamiltonians characterized by the topological invariant $\bar{e}_2$, we reveal that multiple gapless boundary states exist at the domain walls of the surface mass, which give rise to the multiple chiral hinge modes. We also show that three-dimensional insulators characterized by $\bar{e}_2=N$ support $N$ chiral hinge modes. Notably, due to the constraint of two occupied bands in our system, these phases are distinct from stacked Chern insulators composed of $N$ layers. Furthermore, we construct tight-binding models for $\bar{e}_2=2$ and $3$ and numerically demonstrate the emergence of two and three chiral hinge modes, respectively. These results are consistent with those obtained from the surface theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26271 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Euler band topology and multiple hinge modes in three-dimensional insulators Tanaka, Yutaro Kobayashi, Shingo Mesoscale and Nanoscale Physics In two-dimensional systems with space-time inversion symmetry, such as $C_{2z}T$, the reality condition on wave functions gives rise to real band topology characterized by the Euler class, a $\mathbb{Z}$-valued topological invariant for a pair of real bands in the Brillouin zone. In this paper, we study three-dimensional $C_{2z}T$-symmetric insulators characterized by $\bar{e}_2$, defined as the difference in the Euler classes between two $C_{2z}T$-invariant planes in the three-dimensional Brillouin zone. By deriving effective surface Hamiltonians from generic low-energy continuum Hamiltonians characterized by the topological invariant $\bar{e}_2$, we reveal that multiple gapless boundary states exist at the domain walls of the surface mass, which give rise to the multiple chiral hinge modes. We also show that three-dimensional insulators characterized by $\bar{e}_2=N$ support $N$ chiral hinge modes. Notably, due to the constraint of two occupied bands in our system, these phases are distinct from stacked Chern insulators composed of $N$ layers. Furthermore, we construct tight-binding models for $\bar{e}_2=2$ and $3$ and numerically demonstrate the emergence of two and three chiral hinge modes, respectively. These results are consistent with those obtained from the surface theory. |
| title | Euler band topology and multiple hinge modes in three-dimensional insulators |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2603.26271 |