For decades, physics students have been taught two seemingly incompatible rules. Topological phases of matter, celebrated for their extraordinary robustness, owe their stability to an energy gap that separates the bulk states of a material from one another. Critical points, the delicate thresholds where continuous phase transitions occur, are defined by the complete closure of that very gap. One framework demands a gap; the other destroys it. Now two independent experiments, both published in the journal Nature and both guided by the theoretical work of Prof. Xue-Jia Yu of the Eastern Institute of Technology, Ningbo, have demonstrated that topology can survive precisely where it was long assumed to vanish. The results, emerging from collaborations led by Prof. Baile Zhang at Nanyang Technological University in Singapore and Prof. Jianhua Jiang at the University of Science and Technology of China, mark the first experimental confirmation of what researchers call critical topology.

To appreciate why this breakthrough matters, it helps to revisit what topology means in modern physics. Unlike conventional phases of matter, whose identities are dictated by symmetry, topological phases are characterized by global properties that remain unchanged under continuous deformation. The classic analogy compares a coffee mug and a doughnut: each possesses exactly one hole, and one can be smoothly reshaped into the other without tearing or gluing. Because these global properties are quantized, they resist small perturbations. The quantum Hall effect and topological insulators, whose discovery was recognized by the 2016 Nobel Prize in Physics, exploit this robustness to sustain conducting edge states that persist even in the presence of impurities and disorder, so long as the underlying symmetry is preserved.

That robustness, however, has always come with a strict prerequisite. The topological invariant that protects edge states is only well defined when the bulk of the material possesses an energy gap. Close the gap, the standard reasoning goes, and the invariant loses meaning, the edge states disappear, and the phase loses its topological character. This assumption has been so deeply embedded in the field that the very definition of a topological phase has been tied to gapped systems. Generations of researchers have treated the energy gap not as a convenience but as an essential ingredient of topological order.

Criticality occupies the opposite corner of the physics landscape. At a critical point, such as the boiling of water into vapor or the loss of magnetism at the Curie temperature, the energy gap closes completely, microscopic details are washed out, and only long-wavelength collective behavior remains. Remarkably, materials with entirely different microscopic structures can exhibit identical critical exponents at such points, placing them in the same universality class. This universality, honored by the 1982 Nobel Prize in Physics, is one of the most profound insights in science: near criticality, diverse systems converge on a single universal description. But that description is continuous and fluctuation-dominated, while topology is discrete and invariant-protected. For decades the two frameworks were regarded as separate domains that developed independently with little overlap.

Challenging that boundary required years of theoretical groundwork. The question of whether topology could survive at a critical point was once considered a fundamental challenge to the conventional understanding of topological phases. In recent years, Prof. Yu and collaborators systematically explored the possibility through a series of theoretical studies. In 2022 they proposed a classification theory for topology at quantum critical points, published in Physical Review Letters. In 2024 they introduced a generalized topological bulk–edge correspondence applicable to critical points, and in 2026 they extended the theory to nonequilibrium dynamics, work highlighted as an Editor’s Suggestion. Together with Prof. Limei Xu of Peking University and Chair Professor Hai-Qing Lin of Zhejiang University, Yu also authored the first comprehensive review of the field in Physics Reports, consolidating the complete theoretical framework of critical topology.

Turning that framework into laboratory reality posed an entirely different order of difficulty. To realize critical topology in a physical system, researchers must tune the system with extreme precision to a critical point where the bulk becomes completely gapless, and then detect the signatures of topological edge states against strong fluctuations and background noise. The challenge has been compared to stopping a high-speed train exactly at the edge of a cliff while still measuring a tiny speck of dust on one of its wheels. For years, the predictions of critical topology therefore remained confined to theoretical studies and numerical simulations, with no experimental platform able to meet the twin demands of critical tuning and topological resolution.

That changed with two experiments built on acoustic metamaterials, artificial structures in which sound waves mimic the behavior of quantum systems. In the first study, titled Observation of critical topological phase transition, the team led by Prof. Baile Zhang at Nanyang Technological University observed topological zero-energy modes and π modes at a one-dimensional Floquet critical point. The experiment relied on a periodically driven dimerized lattice, the Floquet SSH α-chain, in which two distinct half periods alternately host only next-nearest-neighbor and nearest-neighbor couplings. In the acoustic implementation, a waveguide array maps the propagation direction of sound onto an effective time coordinate, with straight connecting tubes engineering nearest-neighbor coupling and curved tubes implementing next-nearest-neighbor coupling. The work grew out of a theoretical framework proposed by Yu and developed further with collaborators, published in Communications Physics in 2025. Co-first authors are Dr. Zheyu Cheng of Nanyang Technological University and Dr. Xiuhai Zhang of Northwestern Polytechnical University, with co-corresponding authors including Yu, Prof. Longwen Zhou of Ocean University of China, Prof. Jiangbin Gong of the National University of Singapore, and Prof. Zhang.

The second study, titled Experimental observation of critical topology, took a fundamentally different route. The team led by Prof. Jianhua Jiang at the University of Science and Technology of China applied the generalized Li–Haldane bulk–edge correspondence proposed by Yu in recent publications in Physical Review B and Physical Review Research. Rather than probing the energy spectrum directly, the experimenters measured the entanglement spectrum, a quantity drawn from quantum information theory that encodes the pattern of quantum correlations in a system. Using a pump-probe protocol on a one-dimensional phononic crystal, they measured the local response, extracted band dispersions and Bloch wavefunctions through singular-value decomposition, constructed a k-space correlation matrix, and transformed it into real space to obtain the entanglement spectrum. In the nontrivial case, a pair of mid-gap modes at exactly half filling appeared, providing direct experimental evidence for nontrivial critical topology in both one and two dimensions. Co-first authors are Dr. Zhikang Lin of The University of Hong Kong, Mr. Liwei Wang of the University of Science and Technology of China, and Dr. Zelín Kong of Soochow University, with co-corresponding authors Yu, Prof. Shuang Zhang of The University of Hong Kong, and Prof. Jiang.

The significance of having two papers in the same journal issue, built on two independent experimental platforms with different design strategies and measurement approaches, yet resting on the same theoretical origin, is difficult to overstate. Together they provide the first experimental evidence in real physical systems that topology can survive even when the energy gap closes, and that critical universal behavior and topological properties can coexist in the same system. Prof. Yu, serving as co-corresponding author on both papers, provided key theoretical guidance spanning modeling, mechanism interpretation, and the physical picture underlying both experiments. The convergence of independent experimental confirmation with a unified theoretical framework transforms critical topology from a speculative mathematical possibility into an established empirical phenomenon.

The implications extend well beyond the acoustic platforms used in these demonstrations. Critical topology opens new avenues for topological quantum computation, where robust states at criticality could offer novel protection schemes, for the design of new acoustic devices that exploit topology without requiring gapped bulk bands, and for the study of nonequilibrium topological phases of matter, where driven and fluctuating systems are the norm rather than the exception. Topology and criticality, two pillars of physics long considered fundamentally incompatible, have now met in the laboratory, and the theoretical force behind that convergence came from the Eastern Institute of Technology, Ningbo. The research group led by Prof. Yu, which focuses on quantum phase transitions and critical phenomena in strongly correlated many-body systems using tools ranging from conformal field theory to tensor networks and quantum Monte Carlo simulations, has spent the past five years at the forefront of this emerging field, and these two Nature papers represent its most striking vindication to date.

Subject of Research: Experimental observation of critical topology in acoustic metamaterials

Article Title: Breaking a long-standing boundary in physics: Xue-Jia Yu’s team and collaborators publish two consecutive papers in Nature, revealing that topology can survive at critical points

Article References: Breaking a long-standing boundary in physics: Xue-Jia Yu’s team and collaborators publish two consecutive papers in Nature, revealing that topology can survive at critical points. (n.d.). Original publication

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Keywords: critical topology, topological phases, phase transitions, acoustic metamaterials, Floquet systems, entanglement spectrum, bulk-edge correspondence, energy gap, quantum criticality, Nature, Xue-Jia Yu, condensed matter physics