Scattering description of edge states in Aharonov-Bohm triangle chains

Fuente: arXiv
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Main Authors: Liu, Zhi-Hai, Entin-Wohlman, O., Aharony, A., You, J. Q., Xu, H. Q.
Format: Preprint
Published: 2023
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_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