13 April 2023 Thu 5 pm

Non-Hermitian physics has been the focus of much current research, uncovering a wide range of phenomena richer than the Hermitian picture. A unique feature of NH systems, for instance, is the accumulation of an extensive number of eigenstates at the boundaries, a phenomenon termed non-Hermitian skin effect (NHSE). Underpinning the NHSE lies an extreme sensitivity of the spectrum to boundary conditions, which opens up not only new theoretical paradigms, but also new potential avenues for sensor applications. In this talk, I will explore an anomalous skin effect featuring scale-free localization at strong non-Hermitian impurities. The skin effect is termed “anomalous” because its behavior qualitatively differs from the NHSE occurring at open boundaries. Its eigenstate localization is namely not dictated by the bulk and the localization length is not fixed but instead proportional to the system size. I will present this anomalous skin effect in conjunction with potential disorder and explain the emergence of boundary localization by exactly solving a minimal lattice model. In the minimal model, the presence of anisotropic hopping terms can induce a scale-free accumulation of all eigenstates opposite to the bulk hopping direction. While this counterintuitive behavior is fine-tuned and further increasing the hopping weakens and eventually reverses the effect, the interplay with bulk potential disorder dramatically enriches this phenomenology and leads to a robust non-monotonic localization behavior. Scale-free localization is also shown to persist even when the bulk is entirely Hermitian, both in the clean and disordered cases. These results corroborate the potential for harnessing impurities and disorder for local sensing and control of a large class of effectively non-Hermitian systems, and should be readily realizable in numerous state-of-the-art experimental setups implementing non-Hermitian physics, such as in photonic, mechanical, or acoustic systems.

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