Topological insulators on complex networks
Abstract
The landscape of topological insulators has expanded beyond its traditional domain of periodic lattices with short-range hopping. Related studies have explored topological phenomena under non-Euclidean geometries, disordered structures, and long-range hopping, progressively narrowing the gap between topological phases of matter and complex networks. Here we demonstrate that genuine complex networks, far beyond periodic lattices and their conventional variants, can themselves host topological insulating phases. By developing a nonconflicting design framework for multiple topological objectives, we realize topological insulators in high-degree Hofstadter lattices and across regular, small-world, and random networks. This generalization uncovers distinct network-specific features, including an expanded range of attainable topological characteristics, a degree-dependent transition from Hofstadter-type to Haldane-type Chern insulators, and, most notably, the superior robustness and reconfigurability of small-world topological insulators. Our graph-theoretic framework establishes network complexity as a resource for realizing high-capacity and reconfigurable topological insulators.
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BibTeX
@misc{yu2026topological,
title = {{Topological insulators on complex networks}},
author = {Sunkyu Yu and Xianji Piao and Namkyoo Park},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02888},
eprint = {2610.02888},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02888},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Topological insulators on complex networks
AU - Sunkyu Yu
AU - Xianji Piao
AU - Namkyoo Park
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.02888
UR - https://arxiv.org/abs/2610.02888
AB - The landscape of topological insulators has expanded beyond its traditional domain of periodic lattices with short-range hopping. Related studies have explored topological phenomena under non-Euclidean geometries, disordered structures, and long-range hopping, progressively narrowing the gap between topological phases of matter and complex networks. Here we demonstrate that genuine complex networks, far beyond periodic lattices and their conventional variants, can themselves host topological insulating phases. By developing a nonconflicting design framework for multiple topological objectives, we realize topological insulators in high-degree Hofstadter lattices and across regular, small-world, and random networks. This generalization uncovers distinct network-specific features, including an expanded range of attainable topological characteristics, a degree-dependent transition from Hofstadter-type to Haldane-type Chern insulators, and, most notably, the superior robustness and reconfigurability of small-world topological insulators. Our graph-theoretic framework establishes network complexity as a resource for realizing high-capacity and reconfigurable topological insulators.
ER -