Higher-Order Flatband-Touching Points Mediate Unconventional Bulk-Boundary Correspondence
Abstract
The bulk-boundary correspondence establishes a fundamental connection between bulk band topology and the emergence of boundary states, underpinning topological phenomena across electronic, acoustic, photonic, and many other wave systems. A broad class of singular flatband systems, however, exhibits an unconventional form of bulk-boundary correspondence, in which robust boundary modes (RBMs) originate from flatband-touching points (FBTPs) and the real-space topology associated with incomplete sets of compact localized states (CLSs), rather than conventional momentum-space bulk topological invariants. To date, experimental studies of such boundary modes have been limited to systems hosting lower-order FBTPs. Here, we experimentally demonstrate unconventional bulk-boundary correspondence in a photonic cross-bedded Kagome-like lattice featuring a higher-order FBTP formed by the touching of two degenerate flatbands and a dispersive band. Using continuous-wave laser writing, we observe shape-preserving propagation of both bulk CLSs and boundary RBMs. Remarkably, unlike previously reported flatband systems, the RBMs retain their boundary localization under input-field perturbations involving both singular and nonsingular CLSs, revealing an unconventional boundary response associated with the higher-order FBTP in this lattice. Our results establish the Kagome-like lattice as a new platform for exploring flatband physics and unconventional bulk-boundary correspondence, with potential applications in wave localization, flatband lasers, and other emerging topological photonic devices.
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BibTeX
@misc{song2026higherorder,
title = {{Higher-Order Flatband-Touching Points Mediate Unconventional Bulk-Boundary Correspondence}},
author = {Limin Song and Jianqi Xiong and Liqin Tang and Daohong Song and Zhigang Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29251},
eprint = {2610.29251},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29251},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Higher-Order Flatband-Touching Points Mediate Unconventional Bulk-Boundary Correspondence
AU - Limin Song
AU - Jianqi Xiong
AU - Liqin Tang
AU - Daohong Song
AU - Zhigang Chen
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29251
UR - https://arxiv.org/abs/2610.29251
AB - The bulk-boundary correspondence establishes a fundamental connection between bulk band topology and the emergence of boundary states, underpinning topological phenomena across electronic, acoustic, photonic, and many other wave systems. A broad class of singular flatband systems, however, exhibits an unconventional form of bulk-boundary correspondence, in which robust boundary modes (RBMs) originate from flatband-touching points (FBTPs) and the real-space topology associated with incomplete sets of compact localized states (CLSs), rather than conventional momentum-space bulk topological invariants. To date, experimental studies of such boundary modes have been limited to systems hosting lower-order FBTPs. Here, we experimentally demonstrate unconventional bulk-boundary correspondence in a photonic cross-bedded Kagome-like lattice featuring a higher-order FBTP formed by the touching of two degenerate flatbands and a dispersive band. Using continuous-wave laser writing, we observe shape-preserving propagation of both bulk CLSs and boundary RBMs. Remarkably, unlike previously reported flatband systems, the RBMs retain their boundary localization under input-field perturbations involving both singular and nonsingular CLSs, revealing an unconventional boundary response associated with the higher-order FBTP in this lattice. Our results establish the Kagome-like lattice as a new platform for exploring flatband physics and unconventional bulk-boundary correspondence, with potential applications in wave localization, flatband lasers, and other emerging topological photonic devices.
ER -