Disordered Higher-Order Topological Insulator Maintains Corner States until T, Enabling Real-Space Mapping of Boundary Protection

Higher-order topological insulators represent a new frontier in materials science, promising stable, lower-dimensional states that could revolutionise device design, but their vulnerability to disorder remains a significant challenge. Johannes Düreth, Simon Widmann, Philipp Gagel, and colleagues at the University of Würzburg now demonstrate the surprising resilience of these states in a disordered system.

The team investigates a two-dimensional polariton lattice, employing a novel technique called the spectral localizer to map the real-space topology and directly quantify the protection of these states. Their experiments reveal that corner states persist even with substantial disorder, lasting until the material’s spectral gap closes, and the spectral localizer accurately predicts this critical point, offering a powerful tool for designing robust, disorder-resilient devices for applications such as lasing and light-routing. NbTe2 Exhibits Robust Higher-Order Topology Scientists have discovered a robust higher-order topological phase in niobium telluride (NbTe2), a material with potential for novel quantum technologies. This work establishes the existence of zero-dimensional states confined to the corners of one-dimensional domains within the material, exhibiting a unique energy dispersion distinct from conventional edge states. The research combines experimental techniques, including angle-resolved photoemission spectroscopy and scanning tunnelling spectroscopy, with theoretical modelling based on tight-binding calculations and first-principles density functional theory to comprehensively investigate this phenomenon. Detailed analysis of the electronic band structure and spatial mapping of the local density of states demonstrates that these corner states are topologically protected and remain stable even with imperfections. The research reveals a strong connection between the higher-order topological phase and the charge density wave order present in NbTe2, suggesting a novel method for tuning and controlling topological states. This finding is significant because the higher-order topological phase persists even with strong electron interactions, a condition that often destroys topological order in other materials. By incorporating many-body effects into their theoretical calculations, the team accurately reproduces experimental observations and provides a comprehensive understanding of the underlying physics, opening new avenues for exploring correlated topological materials and designing robust quantum devices for applications in spintronics and quantum computing. Topological Photonics and Polariton Investigations Recent research focuses on the rapidly developing field of topological photonics, particularly concerning topological insulators, higher-order topological insulators, and their applications in manipulating light. A key area of investigation concerns the robustness of these topological states in the presence of disorder, such as imperfections or randomness within the material. Researchers are also exploring systems that deviate from standard physics, known as non-Hermitian systems, and their connection to topological phenomena. Several studies investigate the potential for nonlinear optical effects and the creation of topological lasers, with a growing trend towards developing practical devices for wave routing and controlling light flow using these advanced materials. Recent work also explores topological phases in systems lacking long-range crystalline order, expanding the possibilities for material design. These investigations suggest several promising research directions, including the development of robust topological devices, quantum computing with polaritons, tunable topological photonics, and topological photonics in disordered systems. Advanced characterization techniques are also being developed to visualize and characterize these complex topological states. Disorder Tolerance in Higher-Order Topological Insulators Scientists have made a significant advance in understanding how resilient higher-order topological insulators are to imperfections. This work focuses on a two-dimensional polariton lattice engineered to mimic a specific model hosting unique corner and edge states. Experiments reveal that these higher-order boundary states remain remarkably stable, persisting until the strength of introduced disorder reaches approximately one quarter of the system’s spectral gap, establishing a clear threshold for disorder tolerance.

The team developed a novel framework called the spectral localizer to map and quantify topological protection in real space, moving beyond traditional methods that rely on momentum-space classifications. This method accurately identifies the precise disorder strength at which the bandgap closes, effectively predicting the point of instability for the corner states. Measurements confirm that the spectral localizer functions as a predictive tool for any finite-size system, offering a robust means of assessing topological protection in complex, disordered environments. Spectroscopic investigation of the unperturbed lattice revealed the characteristics of the engineered system, demonstrating a transition from a trivial to a topological phase dependent on the ratio of intra-cell to inter-cell hopping parameters.

This research broadens the design principles for higher-order topological insulators and paves the way for implementing robust devices for applications such as lasing, light-routing, and potentially quantum computation. Disorder Resilience of Topological Photonic States This research demonstrates the persistence of robust, higher-order topological states in a disordered photonic lattice, extending the principles of topological insulator design. Scientists successfully mapped and quantified the protection of these states, specifically corner and edge modes, using a novel spectral localizer framework that links crystalline symmetries to real-space characteristics.

The team experimentally introduced controlled disorder into the lattice and observed that the corner states remained stable until the spectral gap closed, corresponding to a disorder strength approximately one quarter of the gap size, establishing the spectral localizer as a predictive tool for assessing the robustness of topological states in finite systems. These findings broaden understanding of how disorder impacts higher-order topological insulators and offer a pathway towards designing more resilient devices for applications such as robust lasing and light-routing. The authors acknowledge that the study focused on a specific type of disorder and lattice configuration, and future work could explore the effects of different disorder types and lattice geometries. Further research may also investigate the potential for actively controlling disorder to manipulate and enhance the properties of these topological states, potentially leading to new functionalities in photonic devices. 👉 More information 🗞 Probing Local Topology in a Disordered Higher-Order Topological Insulator 🧠 ArXiv: https://arxiv.org/abs/2511.13958 Tags: