Fractal hierarchy enables exponential scaling of topological boundary states.

Limin Song, Zhichan Hu, Ziteng Wang, Domenico Bongiovanni, Liqin Tang, Daohong Song, Roberto Morandotti, Jingjun Xu, Hrvoje Buljan, Zhigang Chen

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Article in Nature communications, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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10 authors.

Limin Song *The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin, 300457, China.ORCID http://orcid.org/0000-0002-5094-4013

Zhichan Hu *The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin, 300457, China.ORCID http://orcid.org/0009-0009-3234-4602

Ziteng WangThe MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin, 300457, China.

Domenico BongiovanniThe MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin, 300457, China.

Liqin TangThe MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin, 300457, China.ORCID http://orcid.org/0000-0001-8029-7091

Daohong SongThe MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin, 300457, China.ORCID http://orcid.org/0000-0001-9786-8209

Roberto MorandottiINRS-EMT, 1650 Blvd. Lionel-Boulet, Varennes, Quebec, J3X 1S2, Canada.

Jingjun XuThe MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin, 300457, China.ORCID http://orcid.org/0000-0002-2509-0175

Hrvoje BuljanThe MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin, 300457, China. hbuljan@phy.hr.ORCID http://orcid.org/0000-0002-9808-6628

Zhigang ChenThe MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin, 300457, China. zgchen@nankai.edu.cn.ORCID http://orcid.org/0000-0001-7050-9943

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6 · The paper itself

Abstract

Exponential growth describes an extremely rapid process ubiquitous in mathematics and across diverse physical, biological, and technological systems. Here, we introduce a class of fractal-inspired lattices that combine long-range periodic order with self-similar hierarchy, establishing a structural motif that enables exponential scaling of topological boundary states. We demonstrate this phenomenon in (i) a quasi-one-dimensional lattice chain constructed from Koch-curve unit cells and (ii) a two-dimensional periodic tiling lattice composed of Sierpiński-gasket unit cells. We show that, for suitable coupling parameters, both the number of topological boundary states

Identifiers

PMID42425987

DOI10.1038/s41467-026-75412-y

PMCPMC13478344

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