Topological Zero Modes in Non-Hermitian Topolectrical Systems: Size and Impedance Control
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| Format: | Preprint |
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2025
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| author | Rafi-Ul-Islam, S M Siu, Zhuo Bin Razo, Md. Saddam Hossain Jalil, Mansoor B. A. |
| author_facet | Rafi-Ul-Islam, S M Siu, Zhuo Bin Razo, Md. Saddam Hossain Jalil, Mansoor B. A. |
| contents | We investigate the size-dependent behavior of topological zero modes (TZMs) in finite non-Hermitian Su-Schrieffer-Heeger (SSH) chains implemented on a topolectrical circuit platform. By deriving exact analytical solutions for the eigenenergies and band gaps of TZMs, we reveal their sensitivity to system size and non-Hermitian parameters, such as asymmetric coupling and onsite gain or loss. Our results show that non-Hermiticity enables the recovery of exactly zero-energy TZMs at a critical system size, unlike Hermitian systems where finite-size effects cause energy splitting. These zero-energy modes produce pronounced impedance peaks in the circuit's admittance spectrum, providing a measurable signature of topological states. Additionally, a tunable grounding capacitor enables precise control of TZM energies at a fixed resonance frequency, enhancing practical tunability. Our findings offer insights into finite-size effects in non-Hermitian topological systems and guide the design of robust, reconfigurable topolectrical circuits for sensing and energy transfer applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17227 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological Zero Modes in Non-Hermitian Topolectrical Systems: Size and Impedance Control Rafi-Ul-Islam, S M Siu, Zhuo Bin Razo, Md. Saddam Hossain Jalil, Mansoor B. A. Mesoscale and Nanoscale Physics Atomic and Molecular Clusters We investigate the size-dependent behavior of topological zero modes (TZMs) in finite non-Hermitian Su-Schrieffer-Heeger (SSH) chains implemented on a topolectrical circuit platform. By deriving exact analytical solutions for the eigenenergies and band gaps of TZMs, we reveal their sensitivity to system size and non-Hermitian parameters, such as asymmetric coupling and onsite gain or loss. Our results show that non-Hermiticity enables the recovery of exactly zero-energy TZMs at a critical system size, unlike Hermitian systems where finite-size effects cause energy splitting. These zero-energy modes produce pronounced impedance peaks in the circuit's admittance spectrum, providing a measurable signature of topological states. Additionally, a tunable grounding capacitor enables precise control of TZM energies at a fixed resonance frequency, enhancing practical tunability. Our findings offer insights into finite-size effects in non-Hermitian topological systems and guide the design of robust, reconfigurable topolectrical circuits for sensing and energy transfer applications. |
| title | Topological Zero Modes in Non-Hermitian Topolectrical Systems: Size and Impedance Control |
| topic | Mesoscale and Nanoscale Physics Atomic and Molecular Clusters |
| url | https://arxiv.org/abs/2507.17227 |