In a square lattice built from tiny magnetic rods, light is not merely a wave; it’s a traveler navigating a city laid out by symmetry and magnetism. The traveler’s routes aren’t dictated only by the bulk of the material but by the way the city is cut and rearranged. A new study from Nanyang Technological University in Singapore, led by Hongyu Chen, shows that turning a two-dimensional photonic crystal into an obstructed atomic insulator can conjure bright, stubborn corners where light gets trapped. It isn’t magic; it’s geometry talking to the topological rules that govern wave behavior at edges and corners.
The paper speaks the real-space language of topological quantum chemistry, a framework that asks a deceptively simple question: when does a lattice stop behaving like a normal insulator and begin hosting extra, localized states at its corners? The answer hinges on where you imagine the atoms could sit, not just on which atoms sit there. In the photonic playground of this study, the team demonstrates that corner states—the hallmarks of higher-order topology—emerge only when the lattice exposes particular Wyckoff positions. The result is a reminder that the atoms in a crystal aren’t inert furniture; they shape how light can be confined, steered, and trapped in surprisingly pocketed ways.
The significance isn’t limited to clever optical tricks. It’s a bridge between two ideas that rarely meet in everyday devices: obstructed atomic insulators, a class born from how electrons “want” to sit in a lattice, and higher-order topological insulators, a family of phases where the obvious boundary states hide deeper topological structure at corners or hinges. The researchers used a photonic platform to translate a very theoretical vocabulary into tangible, visible behavior. The work, conducted at NTU Singapore, shows that by arranging magnetic rods and manipulating which parts of the lattice are exposed, you can engineer corner localization with a degree of control that feels almost architectural. The lead author, Hongyu Chen, and colleagues demonstrate that the geometry of the lattice—the real-space distribution of potential sites—can be the decisive ingredient for corner physics.
What makes photonic OAIs different from ordinary insulators
Topological quantum chemistry, the conceptual backbone of the study, classifies topological phases not just by abstract numbers but by the real-space fingerprints left by where electrons or photons prefer to reside. In ordinary insulators, you can often describe the state by where the charges sit in the lattice; in obstructed atomic insulators (OAIs), the situation is more subtle. The lattice appears topologically trivial from a bulk perspective, yet the centers of charge—the Wannier centers—are “obstructed” from sitting where atoms actually sit. That obstruction is a hidden lead in the story: if you cut the material through those obstructed centers, new, often metallic edge states can appear; under the right conditions, corner states even pop out where two edges meet.
In the photonic version explored by Chen’s team, the actors are not electrons but magnetized rods that interact with light in a gyromagnetic medium. The square lattice they build hosts eight elements per unit cell, arranged so that four have one magnetization direction and four the opposite. This arrangement is more than cosmetic: it creates a controlled environment where the photonic bands and the real-space positions of the potential centers interplay in a way that mirrors the mathematics of OAIs. The researchers show that when the lattice is carved so that a particular obstructed Wannier center—what the paper calls the obstructed Wannier charge center (OWCC)—sits at an exposed position labeled 2b, in-gap corner states emerge. If that 2b position isn’t exposed at the edge, the corner states disappear. It’s a delicate, geometry-driven phenomenon, not a bulk property you can predict by looking at the interior alone.
One striking feature the study emphasizes is that corner states in this photonic OAI do not require time-reversal symmetry. By arranging all the magnetic rods in a single magnetization direction, the authors show that breaking or preserving a time-reversal-like symmetry in this photonic context isn’t the controlling factor. The doorway to corner localization is opened by the real-space arrangement of the rods and the way the crystal is cut, not by a global symmetry proxy. That insight nudges us toward a more nuanced view of how to design devices that rely on corner modes: geometry can trump some symmetry considerations in practical terms.
Wyckoff positions as the hidden blueprint for corners
To translate the mathematics into something you can see, the team sets up a pair of photonic units that differ only by which Wyckoff positions are exposed at the edge: 4c versus 2b. Wyckoff positions are, in essence, the blueprint of a crystal’s internal symmetry—locations that can host an influence on the electronic or photonic states due to how the lattice repeats itself. In their square lattice, exposing 4c or 2b changes how the boundary “talks” to the rest of the lattice. When the boundary cuts through an OWCC at 4c, you get clean edge states, but corner states don’t necessarily appear unless the 2b sites are also exposed in a particular way. It’s as if the lattice carries a built-in set of doorways, and which ones you open determines whether a corner can trap light.
In the actual experiments and simulations, the researchers show that opening 2b at the edge creates a pair of in-gap corner states with strikingly localized real-space profiles. These two corner states sit at specific frequencies within the photonic band gap and have nearly identical spatial patterns, a telltale sign of their topological origin. When the number of exposed 2b positions is reduced, or when the 2b positions no longer lie on the edge, those corner states vanish. The result is a vivid demonstration of how the microscopic placement of potential sites—a geometric and crystallographic detail—governs macroscopic wave behavior.
But the study doesn’t stop at a single geometric tweak. The authors explore how rotating the square lattice, effectively changing the crystal orientation, reshapes the corner-state landscape. They compare orientations labeled (100), (110), and (120), each preserving different symmetry subgroups (such as C2T or C4). Their conclusion is provocative: corner states do not survive purely because a single symmetry is preserved; they endure because the combination of exposed Wyckoff positions and lattice orientation aligns with a specific symmetry—C2T in some configurations—while failing in others. In short, symmetry matters, but only in the service of the geometry’s real-space story.
To probe what actually governs the presence or absence of corner modes, the authors also vary a photonic parameter—the gyromagnetic ratio—that tunes how strongly time-reversal-like effects appear. They find that flipping the sign of this parameter does not erase the corner states, reinforcing the lesson that the decisive ingredient is the boundary’s exposure of obstructed centers, not a global symmetry baton passed along by the magnetization direction. The result is a nuanced, almost architectural principle: the corner that lights up is the corner whose boundary reveals the OWCC that the lattice has chosen to obstruct.
Symmetry, orientation, and the surprising role of crystal geometry
What makes this work feel fresh is the insistence on geometry as the primary designer. In many topological systems, the robustness of edge or corner modes often rides on a strict set of symmetries. Here, the photonic crystal showcases corner states even when the conventional symmetry story is bent or broken. The corner modes persist across a range of practical perturbations, as long as the real-space distribution of the lattice’s potential centers—the Wyckoff positions—remains capable of exposing the obstructed Centers at the boundary. That means a device engineer can think in terms of “which corners do I reveal?” rather than “which symmetry must I keep.” The authors illustrate this through a sequence of simulations and experiments that rotate the lattice, alter which sites are exposed, and tweak the gyromagnetic parameters. Across these variations, the emergence or disappearance of corner states tracks the boundary’s relationship to the OWCC, not a fixed symmetry rule.
They also connect their photonic demonstration to the broader idea of higher-order topological insulators (HOTIs). In a HOTI, the bulk might be insulating and the edge might not carry current, but at lower-dimensional boundaries—like corners in 2D—the system can host localized states with special properties. The twist here is that the corner states arise not simply from a bulk topological invariant in momentum space but from a real-space topological classification; an obstructed Wannier center becomes the seed from which corner-localized light grows. It’s a reminder that the full story of topology in materials often spans both the momentum-space narratives and the real-space geometry that actually populates a lattice with potential sites for wave functions to live and die near the edges.
The photonic platform matters, too. Photonic crystals let researchers visualize, in crystal-structure terms, what would otherwise be an abstract topological phase. Light, with its frequency modes and localization patterns, becomes a direct, observable stand‑in for electrons in a solid. The ability to tailor corner states by simply reconfiguring the lattice’s exposed Wyckoff positions is akin to designing a building by choosing which rooms to expose to the street. The street-level exposure—the boundaries—drives what can happen inside, and this work shows that boundary engineering in a photonic lattice can realize, observe, and potentially harness higher-order topology in a highly controllable and tunable way.
Why this matters beyond photonics
Why should curious readers care about all this? Because it reframes how we might design tomorrow’s optical technologies. If corner states can be reliably engineered by boundary geometry rather than by maintaining a narrow swath of symmetries, then photonic devices—lenses, sensors, lasers, and chips—could gain a new kind of robustness and configurability. Corner-localized light is exceptionally well isolated from the bulk modes; it can serve as a tight, on-chip source of photons that doesn’t easily couple to unwanted modes. That has obvious appeal for lasers that want to emit from a single, precise spot or for waveguide networks where light must be confined to tiny corners without leaking into neighboring pathways.
In a broader sense, the work presents a methodological bridge between two communities: the chemistry-and-crystal-structure folks who use topological quantum chemistry to classify phases, and the photonics crowd that builds practical devices out of light. It shows that a concept born in the study of how Wannier centers sit in a lattice can be applied to sculpt real-world optical behavior. If we can map real-space invariants onto robust, device-ready photonic modes, then the dream of topology-inspired photonics becomes less of a theoretical tease and more of a manufacturing blueprint.
Finally, the study invites us to rethink what “robustness” means in a world where devices live in the wild—subject to fabrication imperfections, environmental noise, and imperfect boundaries. The fact that corner states emerge or vanish with the boundary’s exact exposure of Wyckoff positions suggests a design principle: robustness isn’t just about keeping a symmetry intact; it’s about maintaining the boundary geometry that reveals the obstructed centers. In that sense, topology isn’t only about the bulk’s hidden order. It’s a story about how edges, corners, and the spaces between atoms collaborate to shape the fate of light.
In sum, this photonic demonstration of a two-dimensional obstructed atomic insulator from Nanyang Technological University, Singapore, led by Hongyu Chen, adds a vivid chapter to the evolving narrative of higher-order topology. It shows that corner states aren’t merely a quirky curiosity of abstract theory but a tangible phenomenon that can be tuned by geometry, orientation, and boundary design. The broader implication is clear: when you want to trap light at the tiniest of scales,Look to the lattice’s geometry first, and the rest may follow.
