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Interplay of disorder and point-gap topology: Chiral modes, localization, and non-Hermitian Anderson skin effect in one dimension

Sarkar, R and Hegde, SS and Narayan, A (2022) Interplay of disorder and point-gap topology: Chiral modes, localization, and non-Hermitian Anderson skin effect in one dimension. In: Physical Review B, 106 (1).

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Official URL: https://doi.org/10.1103/PhysRevB.106.014207


Symmetry-protected spectral topology in extended non-Hermitian quantum systems has interesting manifestations such as dynamically anomalous chiral currents and skin effect. In this paper, we study the interplay between symmetries and disorder in a paradigmatic model for spectral topology - the nonreciprocal Su-Schrieffer-Heeger model. We consider the effect of on-site perturbations (both real and purely imaginary) that explicitly break the sublattice symmetry. Such symmetry-breaking terms can retain a nontrivial spectral topology but lead to a different symmetry class. We numerically study the effect of disorder in on-site and nonreciprocal hopping terms. Using a real-space winding number that is self-averaging and quantized, we investigate the impact of disorder on the spectral topology and associated anomalous chiral modes under periodic boundary conditions. We discover a remarkable robustness of chiral current and its self-averaging nature under disorder. The value of the chiral current retains the clean system value, is independent of disorder strength, and is tracked completely by the real-space winding number for class A which has no symmetries, and class AIII, which has a sublattice symmetry. In class D†, which has PT-symmetric on-site gain and loss terms, we find that the disorder-averaged current is not robust while the winding number is robust. We study the localization physics using the inverse participation ratio and local density of states. As the disorder strength is increased, a mobility-edge phase with a finite winding appears. The abrupt vanishing of the winding number marks a transition from a partially localized to a fully localized phase. Under open boundary conditions, we similarly observe a series of transitions through skin effect-partial skin effect-no skin effect phases. Further, we study the non-Hermitian Anderson skin effect (NHASE) for different symmetry classes, where the system without skin effect develops a disorder-driven skin effect at intermediate disorder values. Remarkably, while NHASE is present for different classes, the real-space winding number shows a direct correspondence with it only when all symmetries are broken.

Item Type: Journal Article
Publication: Physical Review B
Publisher: American Physical Society
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Boundary conditions; Quantum optics; Topology; Winding, Andersons; Chiral currents; Disorder strength; Hermitians; Nonreciprocal; Real-space; Self averaging; Sublattice symmetry; Symmetry class; Winding number, Skin effect
Department/Centre: Division of Chemical Sciences > Solid State & Structural Chemistry Unit
Division of Physical & Mathematical Sciences > Physics
Date Deposited: 30 Aug 2022 11:53
Last Modified: 30 Aug 2022 11:53
URI: https://eprints.iisc.ac.in/id/eprint/76277

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