In a groundbreaking leap for the field of topological photonics, researchers from Fudan University and the University of Hong Kong have unveiled a revolutionary paradigm that expands the reach of higher-order topological insulators (HOTIs) beyond the confines of traditional lattice systems. Their study, recently published in eLight under the title “Intrinsic Topological Hinge States Induced by Boundary Gauge Fields in Photonic Metamaterials,” brings to light the discovery of intrinsic HOTI-type hinge states emerging from homogeneous electromagnetic media. This marks a radical departure from established frameworks, which primarily depended on carefully engineered discrete lattice models, thus significantly broadening the spectrum of feasible topological platforms.
Topological insulators have long fascinated physicists due to their ability to host robust boundary states intimately tied to the bulk topology of materials. Extending this concept, HOTIs are characterized by boundary phenomena occurring in dimensions two or more lower than their bulk counterparts—most notably manifesting as hinge or corner states. Traditionally, experimental realizations and theoretical designs of HOTIs have been restricted to highly engineered tight-binding lattices, which are limited both in practicality and in their scope of physical platforms. This novel research circumvents these limitations by harnessing continuum, homogeneous photonic metamaterials that effectively simulate higher-dimensional topologies.
The essential breakthrough centers around the concept of a second Chern number ((c_2))—a sophisticated topological invariant defined in synthetic five-dimensional parameter spaces. By designing a homogenous electromagnetic medium with nontrivial (c_2), the team created a platform capable of fostering topological hinge states without relying on underlying lattice symmetries. This synthetic dimensionality is encoded through engineered bianisotropic responses and spatial modulation of electromagnetic parameters, effectively constructing a five-dimensional topological manifold within a three-dimensional metamaterial. The researchers demonstrate that such homogenized media host topologically protected states localized precisely on the hinges of a cylindrical geometry.
A pivotal insight revealed in this work is the role of boundary curvature as an emergent gauge field that couples intricately with surface Weyl points arising naturally from the bulk topology. These Weyl points, situated on a four-dimensional boundary normal to a particular spatial direction, give rise to one-dimensional Weyl arcs linking projections of Yang monopoles—topological singularities characterized by their (c_2) charge. The boundary curvature, acting analogously to a synthetic gauge potential, interacts with these Weyl states to produce spatially localized chiral zero modes. These modes, confined at the hinges of the metamaterial cylinder, epitomize intrinsic HOTI hinge states robust to conventional symmetry-breaking perturbations.
This geometric gauge field mechanism sharply contrasts with the traditional symmetry-protected paradigm in HOTI physics. Previously, the stability and existence of hinge or corner states were predicated on preserving certain discrete symmetries such as time-reversal, parity, or lattice-specific crystallographic symmetries. Here, however, the hinge states owe their protection solely to the higher-dimensional topological invariant (c_2), rendering them fundamentally immune to symmetry disruptions. This topological robustness offers a sizeable advantage, enabling broad material applicability, versatility in shape and size, and resilience against imperfections or disorder in experimental setups.
To rigorously validate their theoretical predictions, the research combined effective medium theory with comprehensive full-wave electromagnetic simulations and analytical modeling. The simulated hinge states were found to be distinctly localized and characterized by Hermite-Gaussian-type spatial field distributions, highlighting their unique spatial confinement and modal structure. Analytical treatments further underscored the topological origin of these modes, confirming that they were indeed intrinsic zero modes, stabilized by the synthetic gauge fields induced by curvature rather than any low-dimensional symmetry constraint.
Experimentally, the team fabricated a photonic metamaterial cylinder constructed from carefully arranged metallic helical structures. These helices were meticulously designed to realize the required medium parameters that yield nontrivial (c_2) topology in an effective five-dimensional synthetic space. Microwave near-field scanning measurements unambiguously detected localized hinge modes existing within the surface bandgap, affirming the theoretical horizon first presented. The measured electromagnetic energy distributions corresponded strikingly with predictions, directly visualizing the four hinge states encircling the perimeter of the cylinder. This formidable experimental demonstration offers compelling evidence for intrinsic HOTI hinge physics in continuum platforms.
Beyond the immediate confirmation of HOTI hinge states in homogeneous metamaterials, this study lays a broad conceptual foundation for future topological designs. By linking geometry, topology, and gauge fields intricately, it hints at a new class of topological phenomena accessible through continuous media engineering, liberating topological photonics from the constraints of lattice symmetry and tight-binding approximations. The synthetic gauge potentials induced by spatial curvature could become a versatile tool for sculpting robust chiral modes, potentially applicable not only in photonics but also in acoustics, mechanics, and electronic metamaterials.
Dr. Shaojie Ma, leading the investigation, highlights that this novel framework bridges geometry and topological physics in unprecedented ways. The emergence of hinge states from curvature-induced gauge fields redefines design principles for higher-order topology, presenting new routes to robust waveguiding, loss-immune optical circuitry, and on-chip topological devices. Such topological waveguides could provide significant advancement for integrated photonics, particularly in environments sensitive to fabrication imperfections or dynamic perturbations.
Importantly, the intrinsic nature of the hinge states means that device designers can leverage a richer variety of materials and structures without stringent symmetry considerations. This transformative result opens avenues for exploiting ordinary continuous media with tailored anisotropies and chiral electromagnetic responses to realize and manipulate topological states. The engineering of synthetic higher-dimensional topologies via electromagnetic parameter spaces also offers a profoundly flexible platform for future discoveries in topological matter.
The research was conducted under the auspices of prominent funding programs including the National Key Research and Development Program of China, the National Natural Science Foundation of China, and the Research Grants Council of Hong Kong, underscoring the strategic importance attributed to topological photonics and metamaterials. Collaborative efforts between Fudan University and the University of Hong Kong were fundamental in merging theoretical insights with cutting-edge experimental implementation, fostering an interdisciplinary approach key to this success.
The findings documented here not only deepen fundamental understanding of topological phases in synthetic dimensions but also hold promise for enabling next-generation photonic technologies that are robust, scalable, and compatible with existing technological ecosystems. The integration of gauge-field mechanisms and higher-dimensional topological invariants could catalyze advances in areas ranging from quantum information processing to nonlinear optics, where control over light-matter interaction at the nanoscale is crucial.
Subject of Research: Higher-order topological insulators and intrinsic hinge states in photonic metamaterials driven by synthetic higher-dimensional topological invariants and boundary gauge fields.
Article Title: Intrinsic topological hinge states induced by boundary gauge fields in photonic metamaterials
Web References: DOI: 10.1186/s43593-025-00097-7
Image Credits: He, C., Zhao, L., Zhang, S. et al.
Keywords
Higher-order topological insulators, HOTI, photonic metamaterials, second Chern number, synthetic dimensions, boundary gauge fields, hinge states, Weyl points, Yang monopole, bianisotropic media, topological robustness, chiral zero modes, waveguides, electromagnetic topology, gauge potential, metamaterial cylinder
