Su-Schrieffer-Heeger chain with one pair of $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric defects

Su-Schrieffer-Heeger chain with one pair of $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric defects

Abstract The topologically nontrivial edge states induce $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 transition in Su-Schrieffer-Heeger (SSH) chain with one pair of gain and loss at boundaries. In this study, we investigated a pair of $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric defects located inside the SSH chain...

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Autores principales: L. Jin, P. Wang, Z. Song
Formato: article
Lenguaje:EN
Publicado: Nature Portfolio 2017
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Science
Q
Acceso en línea:https://doaj.org/article/7585dda186dc41c181d651aa7d77608d
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spelling oai:doaj.org-article:7585dda186dc41c181d651aa7d77608d2021-12-02T15:06:16ZSu-Schrieffer-Heeger chain with one pair of $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric defects10.1038/s41598-017-06198-92045-2322https://doaj.org/article/7585dda186dc41c181d651aa7d77608d2017-07-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-06198-9https://doaj.org/toc/2045-2322Abstract The topologically nontrivial edge states induce $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 transition in Su-Schrieffer-Heeger (SSH) chain with one pair of gain and loss at boundaries. In this study, we investigated a pair of $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric defects located inside the SSH chain, in particular, the defects locations are at the chain centre. The $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 symmetry breaking of the bound states leads to the $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 transition, the $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric phases and the localized states were studied. In the broken $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric phase, all energy levels break simultaneously in topologically trivial phase; however, two edge states in topologically nontrivial phase are free from the influence of the $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric defects. We discovered $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric bound states induced by the $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric local defects at the SSH chain centre. The $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric bound states significantly increase the $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 transition threshold and coalesce to the topologically protected zero mode with vanishing probabilities on every other site of the left-half chain and the right-half chain, respectively.L. JinP. WangZ. SongNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-9 (2017)
institution DOAJ
collection DOAJ
language EN
topic Medicine
R
Science
Q
spellingShingle Medicine
R
Science
Q
L. Jin
P. Wang
Z. Song
Su-Schrieffer-Heeger chain with one pair of $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric defects
description Abstract The topologically nontrivial edge states induce $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 transition in Su-Schrieffer-Heeger (SSH) chain with one pair of gain and loss at boundaries. In this study, we investigated a pair of $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric defects located inside the SSH chain, in particular, the defects locations are at the chain centre. The $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 symmetry breaking of the bound states leads to the $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 transition, the $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric phases and the localized states were studied. In the broken $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric phase, all energy levels break simultaneously in topologically trivial phase; however, two edge states in topologically nontrivial phase are free from the influence of the $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric defects. We discovered $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric bound states induced by the $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric local defects at the SSH chain centre. The $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric bound states significantly increase the $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 transition threshold and coalesce to the topologically protected zero mode with vanishing probabilities on every other site of the left-half chain and the right-half chain, respectively.
format article
author L. Jin
P. Wang
Z. Song
author_facet L. Jin
P. Wang
Z. Song
author_sort L. Jin
title Su-Schrieffer-Heeger chain with one pair of $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric defects
title_short Su-Schrieffer-Heeger chain with one pair of $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric defects
title_full Su-Schrieffer-Heeger chain with one pair of $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric defects
title_fullStr Su-Schrieffer-Heeger chain with one pair of $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric defects
title_full_unstemmed Su-Schrieffer-Heeger chain with one pair of $$\mathcal{P}\mathcal{T}$$ 𝒫 𝒯 -symmetric defects
title_sort su-schrieffer-heeger chain with one pair of $$\mathcal{p}\mathcal{t}$$ 𝒫 𝒯 -symmetric defects
publisher Nature Portfolio
publishDate 2017
url https://doaj.org/article/7585dda186dc41c181d651aa7d77608d
work_keys_str_mv AT ljin suschriefferheegerchainwithonepairofmathcalpmathcaltptsymmetricdefects
AT pwang suschriefferheegerchainwithonepairofmathcalpmathcaltptsymmetricdefects
AT zsong suschriefferheegerchainwithonepairofmathcalpmathcaltptsymmetricdefects
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