Probing Local Topology in a Disordered Higher-Order Topological Insulator
Abstract
Higher-order topology is prized for its ability to realize lower-dimensional boundary states which are stable beyond fine-tuning. However, disorder presents a failure mechanism that can destroy topological in-gap states. Here, we investigate a disordered two-dimensional polariton lattice and employ the spectral localizer framework to define a real-space topological index rooted in crystalline spatial symmetries. This framework enables direct real-space mapping of topology beyond conventional momentum-space classifications, confirming the presence of corner and edge modes in this generalized Su-Schrieffer-Heeger model. Furthermore, it can directly quantify topological protection of a state. We leverage the versatility of our platform to experimentally realize normally distributed, random disorder and find that the corner states persist until the spectral gap closes. Experimentally, this corresponds to a disorder strength of approximately one quarter of the spectral gap. The spectral localizer accurately identifies the disorder strength at which the bandgap closes, establishing the framework as a predictive tool for every finite size system. Our results broaden the design principles for higher-order topological insulators and open the way towards imple menting disorder-resilient devices for robust lasing, light-routing, and quantum computation.
Keywords
Cite
@article{arxiv.2511.13958,
title = {Probing Local Topology in a Disordered Higher-Order Topological Insulator},
author = {Johannes Düreth and Simon Widmann and Philipp Gagel and Siddhartha Dam and Simon Betzold and Monika Emmerling and Christian G. Mayer and David Laibacher and Martin Kamp and Oleg A. Egorov and Ulf Peschel and Tobias Hofmann and Ronny Thomale and Alexander Cerjan and Sven Höfling and Sebastian Klembt},
journal= {arXiv preprint arXiv:2511.13958},
year = {2025}
}