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Non-Hermiticity induced exceptional points and skin effect in the Haldane model on a dice lattice

Sarkar, R and Bandyopadhyay, A and Narayan, A (2023) Non-Hermiticity induced exceptional points and skin effect in the Haldane model on a dice lattice. In: Physical Review B, 107 (3).

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Official URL: https://doi.org/10.1103/PhysRevB.107.035403


The interplay of topology and non-Hermiticity has led to diverse, exciting manifestations in a plethora of systems. In this work, we systematically investigate the role of non-Hermiticity in the Chern insulating Haldane model on a dice lattice. Due to the presence of a nondispersive flat band, the dice-Haldane model hosts a topologically rich phase diagram with the nontrivial phases accommodating Chern numbers ±2. We introduce non-Hermiticity into this model in two ways - through balanced non-Hermitian gain and loss, and by nonreciprocal hopping in one direction. Both these types of non-Hermiticity induce higher-order exceptional points of order three. Remarkably, the exceptional points at high-symmetry points occur at odd integer values of the non-Hermiticity strength in the case of balanced gain and loss, and at odd integer multiples of 1/2 for nonreciprocal hopping. We substantiate the presence and the order of these higher-order exceptional points using the phase rigidity and its scaling. Furthermore, we construct a phase diagram to identify and locate the occurrence of these exceptional points in the parameter space. Non-Hermiticity has yet more interesting consequences on a finite-sized lattice. Unlike for balanced gain and loss, in the case of nonreciprocal hopping, the nearest-neighbor lattice system under periodic boundary conditions accommodates a finite, nonzero spectral area in the complex plane. This manifests as the non-Hermitian skin effect when open boundary conditions are invoked. In the more general case of the dice-Haldane lattice model, the non-Hermitian skin effect can be caused by both gain and loss or nonreciprocity. Fascinatingly, the direction of localization of the eigenstates depends on the nature and strength of the non-Hermiticity. We establish the occurrence of the skin effect using the local density of states, inverse participation ratio, and the edge probability and demonstrate its robustness to disorder. Our results place the dice-Haldane model as an exciting platform to explore non-Hermitian physics. © 2023 American Physical Society.

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; Skin effect; Topology, Exceptional points; Flat band; Haldane model; Hermitians; Hermiticity; High-order; Higher-order; Nonreciprocal; Odd integers; Rich phase, Phase diagrams
Department/Centre: Division of Chemical Sciences > Solid State & Structural Chemistry Unit
Division of Physical & Mathematical Sciences > Physics
Date Deposited: 09 Feb 2023 05:41
Last Modified: 09 Feb 2023 05:41
URI: https://eprints.iisc.ac.in/id/eprint/80107

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