Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910679496130560 |
|---|---|
| author | Lin, Ling Ke, Yongguan Zhang, Li Lee, Chaohong |
| author_facet | Lin, Ling Ke, Yongguan Zhang, Li Lee, Chaohong |
| contents | Chern number is a crucial invariant for characterizing topological feature of two-dimensional quantum systems. Real-space Chern number allows us to extract topological properties of systems without involving translational symmetry, and hence plays an important role in investigating topological systems with disorder or impurity. On the other hand, the twisted boundary condition (TBC) can also be used to define the Chern number in the absence of translational symmetry. Based on the perturbative nature of the TBC under appropriate gauges, we derive the two real-space formulae of Chern number (namely the non-commutative Chern number and the Bott index formula), which are numerically confirmed for the Chern insulator and the quantum spin Hall insulator. Our results not only establish the equivalence between the real-space and TBC formula of the Chern number, but also provide concrete and instructive examples for deriving the real-space topological invariant through the twisted boundary condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_04164 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae Lin, Ling Ke, Yongguan Zhang, Li Lee, Chaohong Quantum Physics Computational Physics Chern number is a crucial invariant for characterizing topological feature of two-dimensional quantum systems. Real-space Chern number allows us to extract topological properties of systems without involving translational symmetry, and hence plays an important role in investigating topological systems with disorder or impurity. On the other hand, the twisted boundary condition (TBC) can also be used to define the Chern number in the absence of translational symmetry. Based on the perturbative nature of the TBC under appropriate gauges, we derive the two real-space formulae of Chern number (namely the non-commutative Chern number and the Bott index formula), which are numerically confirmed for the Chern insulator and the quantum spin Hall insulator. Our results not only establish the equivalence between the real-space and TBC formula of the Chern number, but also provide concrete and instructive examples for deriving the real-space topological invariant through the twisted boundary condition. |
| title | Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae |
| topic | Quantum Physics Computational Physics |
| url | https://arxiv.org/abs/2308.04164 |