S M Rafi-Ul-Islam, Zhuo Bin Siu, Md. Saddam Hossain Razo, Mansoor B.A. Jalil
Lattice models that exhibit topological zero-energy boundary modes show a remarkable sensitivity to the system length and the applied boundary conditions. The exact solutions for the eigenenergies and band gap of the topological modes in a generalized two-band non-Hermitian model on a topolectrical circuit platform are presented, which show an extra-ordinary dependence on the system size. Additionally, it is shown that the introduction of non-Hermiticity results in the recovery of topological modes with the exact eigenenergy of zero at a certain critical system size. Such zero-admittance edge states are reflected in the large impedance peaks in the impedance spectrum. The results reveal that the boundary modes of a non-Hermitian lattice can be tuned via system size.
{"title":"Critical System Size for the Recovery of Topological Zero Modes in Finite Non-Hermitian Systems","authors":"S M Rafi-Ul-Islam, Zhuo Bin Siu, Md. Saddam Hossain Razo, Mansoor B.A. Jalil","doi":"10.1002/andp.202500232","DOIUrl":"https://doi.org/10.1002/andp.202500232","url":null,"abstract":"<p>Lattice models that exhibit topological zero-energy boundary modes show a remarkable sensitivity to the system length and the applied boundary conditions. The exact solutions for the eigenenergies and band gap of the topological modes in a generalized two-band non-Hermitian model on a topolectrical circuit platform are presented, which show an extra-ordinary dependence on the system size. Additionally, it is shown that the introduction of non-Hermiticity results in the recovery of topological modes with the exact eigenenergy of zero at a certain critical system size. Such zero-admittance edge states are reflected in the large impedance peaks in the impedance spectrum. The results reveal that the boundary modes of a non-Hermitian lattice can be tuned via system size.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"537 12","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/andp.202500232","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145698970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the present theoretical work, magnetic response of a tight-binding (TB) dimerized ring subjected to Aharonov–Bohm (AB) flux and environmental interactions is numerically explored. Specifically, an imaginary site potential on the odd lattice sites is introduced to represent physical gain and loss, while the even lattice sites remain unperturbed. The induced current resulting from the AB flux in both real and imaginary eigenspaces, aiming to enhance this current significantly by adjusting the gain/loss parameter (