Isospectrally Patterned Aperiodic Lattices

• URL: http://arxiv.org/abs/2406.18431v2
• Date: Thu, 28 Nov 2024 13:52:59 GMT
• Title: Isospectrally Patterned Aperiodic Lattices
• Authors: Peter Schmelcher,
• Abstract summary: We design and explore patterned aperiodic lattices consisting of coupled isospectral cells that vary across the lattice. The characteristic localization length emerges due to a competition of the involved phase gradient. We outline the perspectives of investigation of this novel class of isospectrally patterned aperiodic lattices.
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• Abstract: We design and explore patterned aperiodic lattices consisting of coupled isospectral cells that vary across the lattice. Each resulting band consists of three distinct energy domains with two mobility edges marking the transition from single center localized to delocalized states and vice versa. The characteristic localization length emerges due to a competition of the involved phase gradient on basis of a local rotation and the coupling between the cells which allows us to understand the localization mechanism and its evolution. The fraction of localized versus delocalized eigenstates can be tuned by changing the gradient between the cells of the lattice. We outline the perspectives of investigation of this novel class of isospectrally patterned aperiodic lattices.

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