Scattering description of edge states in Aharonov-Bohm triangle chains
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913263814443008 |
|---|---|
| author | Liu, Zhi-Hai Entin-Wohlman, O. Aharony, A. You, J. Q. Xu, H. Q. |
| author_facet | Liu, Zhi-Hai Entin-Wohlman, O. Aharony, A. You, J. Q. Xu, H. Q. |
| contents | Scattering theory has been suggested as a convenient method to identify topological phases of matter, in particular of disordered systems for which the Bloch band-theory approach is inapplicable. Here we examine this idea, employing as a benchmark a one-dimensional triangle chain whose versatility yields a scattering matrix that ``flows" in parameter space among several members of the topology classification scheme. Our results show that the reflection amplitudes (from both ends of a sufficiently long chain) do indicate the appearance of edge states in {\it all} (topological and non-topological) cases. For the topological cases, the transmission has a peak at the topological phase transition, which happens at the Fermi energy. A peak still exists as one moves into the non-topological `trivial' regions, in which another transmission peak may occur at nonzero energy, at which a relevant edge state appears in the isolated chain. For finite chains, the peak in the transmission strongly depends on their coupling of the leads, and {\it not} on the phase transition of the isolated chain. In any case, {\it the appearance of a peak in the transmission is not sufficient to conclude that the system undergoes a topological phase transition.} |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05153 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Scattering description of edge states in Aharonov-Bohm triangle chains Liu, Zhi-Hai Entin-Wohlman, O. Aharony, A. You, J. Q. Xu, H. Q. Mesoscale and Nanoscale Physics Scattering theory has been suggested as a convenient method to identify topological phases of matter, in particular of disordered systems for which the Bloch band-theory approach is inapplicable. Here we examine this idea, employing as a benchmark a one-dimensional triangle chain whose versatility yields a scattering matrix that ``flows" in parameter space among several members of the topology classification scheme. Our results show that the reflection amplitudes (from both ends of a sufficiently long chain) do indicate the appearance of edge states in {\it all} (topological and non-topological) cases. For the topological cases, the transmission has a peak at the topological phase transition, which happens at the Fermi energy. A peak still exists as one moves into the non-topological `trivial' regions, in which another transmission peak may occur at nonzero energy, at which a relevant edge state appears in the isolated chain. For finite chains, the peak in the transmission strongly depends on their coupling of the leads, and {\it not} on the phase transition of the isolated chain. In any case, {\it the appearance of a peak in the transmission is not sufficient to conclude that the system undergoes a topological phase transition.} |
| title | Scattering description of edge states in Aharonov-Bohm triangle chains |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2311.05153 |