Impurity induced scale-free localization

By Linhu Li, Ching Hua Lee, J. Gong. 2020

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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. 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.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3f6035709a223c540ee97fc010dbf7713fb689c3