Impurity induced scale-free localization

Non-Hermitian physics describes an open system, which is susceptible to loss or gain and has been recently used to demonstrate unusual physical phenomena in non-trivial topological systems. Here, the authors investigate the physics of impurity effects in non-Hermitian, non-reciprocal lattices and discuss how the results can be realised using an electrical circuit. Non-Hermitian systems have been shown to have a dramatic sensitivity to their boundary conditions. In particular, the non-Hermitian skin effect induces collective boundary localization upon turning off boundary coupling, a feature very distinct from that under periodic boundary conditions. Here we develop a full framework for non-Hermitian impurity physics in a non-reciprocal lattice, with periodic/open boundary conditions and even their interpolations being special cases across a whole range of boundary impurity strengths. We uncover steady states with scale-free localization along or even against the direction of non-reciprocity in various impurity strength regimes. Also present are Bloch-like states that survive albeit broken translational invariance. We further explore the co-existence of non-Hermitian skin effect and scale-free localization, where even qualitative aspects of the system's spectrum can be extremely sensitive to impurity strength. Specific circuit setups are also proposed for experimentally detecting the scale-free accumulation, with simulation results confirming our main findings.

Automated summary

Non-Hermitian physics describes open systems susceptible to loss or gain, and this study investigates impurity effects in such systems, proposing specific circuit setups for experimental verification. The sensitivity of non-Hermitian systems to boundary conditions is explored, revealing steady states with scale-free localization and co-existence of non-Hermitian skin effect and scale-free localization in various impurity strength regimes. Bloch-like states are also observed in the system, showing sensitivity to impurity strength even in qualitative aspects of the system's spectrum. Simulation results confirm the main findings of the study.