Topological Zero Modes in Non-Hermitian Topolectrical Systems: Size and Impedance Control

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.