Scale-Free Non-Hermitian Sensing Enabled by Critical Non-Hermiticity in Topological Systems

We present a novel non-Hermitian sensing scheme demonstrating scale-free responses to boundary perturbations in a two-terminal lattice at critical non-Hermiticity parameters. Unlike traditional non-Hermitian sensing, which exhibits exponential scaling with system size, our model shows a size-independent, linear amplification of boundary perturbations. This phenomenon arises from the delocalization of the topological zero modes (TZMs) at critical non-Hermiticity, whereas the bulk eigenstates remain highly localized by the non-Hermitian skin effect. The linear energy shift induced by boundary perturbations accurately reflects the perturbation strength, enabling precise estimation. Additionally, the closure of the bulk band gap at these parameters under periodic boundaries signifies the onset of critical non-Hermiticity. Our findings are corroborated via LTspice simulations of an equivalent topolectrical circuit, where the impedance spectrum shifts match the energy shift of the TZMs and remain consistent across varying system sizes. This work provides new insights for designing non-Hermitian sensors with scale-free responses for real-world applications.