Critical System Size for the Recovery of Topological Zero Modes in Finite Non‐Hermitian Systems

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.