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arXiv · 2103.08980

Higher-order topological states mediated by long-range coupling in $D_4$-symmetric lattices

Nikita A. Olekhno·Alina D. Rozenblit·Valerii I. Kachin·Alexey A. Dmitriev·Oleg I. Burmistrov·Pavel S. Seregin·Dmitry V. Zhirihin·Maxim A. Gorlach
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Abstract

Topological physics opens a door towards flexible routing and resilient localization of waves of various nature. Recently proposed higher-order topological insulators provide advanced control over wave localization in the structures of different dimensionality. In many cases, the formation of such higher-order topological phases is governed by the lattice symmetries, with kagome and breathing honeycomb lattices being prominent examples. Here, we design and experimentally realize the resonant electric circuit with $D_4$ symmetry and additional next-nearest-neighbor couplings. As we prove, a coupling of the distant neighbors gives rise to an in-gap corner state. Retrieving the associated invariant directly from the experiment, we demonstrate the topological nature of the designed system, revealing the role of long-range interactions in the formation of topological phases. Our results thus highlight the distinctions between tight-binding systems and their photonic counterparts with long-range couplings.

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Nikita A. Olekhno, Alina D. Rozenblit, Valerii I. Kachin, Alexey A. Dmitriev, Oleg I. Burmistrov, Pavel S. Seregin, Dmitry V. Zhirihin, Maxim A. Gorlach. 2021-03-16. Higher-order topological states mediated by long-range coupling in $D_4$-symmetric lattices. https://doi.org/10.1103/physrevb.105.l081107

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