Topological insulators (TIs) have fundamentally reshaped our understanding of materials by introducing robust boundary states arising from bulk topological invariants. Extending this paradigm, higher-order topological insulators (HOTIs), characterized by boundary states of dimension at least two lower than the bulk, have attracted significant attention. However, conventional HOTI realizations mainly rely on discrete, lattice-engineered tight-binding models, which constrain their experimental accessibility and limit integration into continuum platforms.
Now, a research team led by Dr. Shaojie Ma and Prof. Lei Zhou from Fudan University, in collaboration with Prof. Shuang Zhang from the University of Hong Kong, has theoretically predicted and experimentally demonstrated a novel mechanism to realize intrinsic HOTIs in homogeneous photonic metamaterials. Their findings, published in eLight under the title "Intrinsic Topological Hinge States Induced by Boundary Gauge Fields in Photonic Metamaterials," reveal that a homogeneous electromagnetic medium, characterized by a nontrivial second Chern number (𝑐₂) in a synthetic five-dimensional space, can host topologically protected intrinsic HOTI-type hinge states.
The study provides novel insights into the origin of the HOTI-type hinge states, revealing the crucial role of gauge fields induced by boundary curvature. Specifically, the curvature acts as a synthetic gauge potential that couples with surface Weyl points -- topological features that naturally arise from the nontrivial second Chern number (𝑐₂) in a synthetic five-dimensional space. Physically, the interaction between these curvature-induced gauge fields and surface Weyl states leads to the emergence of localized chiral zero modes that manifest as HOTI hinge states.
This novel physical picture stands in sharp contrast to traditional symmetry-protected HOTIs, which typically rely on time-reversal, parity, or crystalline symmetries for their topological protection. In contrast, the newly discovered hinge states are intrinsically protected by the higher-dimensional topological invariant c2 alone. Hence, their existence is independent of specific symmetries, enabling universal applicability across diverse material compositions, geometric configurations, and electromagnetic properties.
By employing effective medium theory, full-wave simulations, and analytical models, the researchers comprehensively explored these phenomena. The hinge modes exhibit unique spatial field distributions, characterized by localized Hermite-Gaussian wavefunctions. Analytical investigation further confirms their topological robustness, demonstrating that these modes are intrinsically protected by higher-dimensional topological invariants, independent of any underlying symmetries.
To experimentally validate this mechanism, the team fabricated a photonic metamaterial cylinder composed of metallic helical structures engineered to realize the required effective medium properties. Microwave near-field measurements confirmed the presence of localized hinge states predicted by theoretical and numerical analyses. The experiments provided clear evidence of hinge states residing within the surface bandgap and exhibiting strongly localized energy distributions.
"This new framework not only provides deeper insights into the interplay between geometry-induced gauge fields and topological invariants," says Dr. Shaojie Ma, "but also opens a novel pathway for realizing HOTIs beyond traditional tight-binding models."
This groundbreaking approach significantly expands the possibilities for practical realizations of topological states in optics and other wave-based systems. It broadens the scope of materials and structural designs capable of supporting higher-order topological phenomena, paving the way toward new technological applications such as robust waveguides, advanced optical devices, and enhanced photonic circuits.
This research received funding from the National Key Research and Development Program of China, the National Natural Science Foundation of China, the start-up funding of Fudan University, the New Cornerstone Science Foundation, the Research Grants Council of Hong Kong, and Guangdong Provincial Quantum Science Strategic Initiative.
