Two Nature Studies Show Topology Can Survive Where the Energy Gap Closes
Acoustic-metamaterial experiments in Singapore and China confirm a long-theorized idea that robust topological states can coexist with a quantum critical point.
Two independent experiments published in Nature have shown that topological states of matter can persist at a critical point, where the material's energy gap closes. For decades physicists treated that combination as impossible. The experiments, run by teams led by Baile Zhang at Nanyang Technological University in Singapore and Jianhua Jiang at the University of Science and Technology of China, both used acoustic metamaterials as an artificial testbed.
The conflict is old. Topological phases, recognized by the 2016 Nobel Prize in Physics, are defined by global properties that stay unchanged when a system is smoothly deformed, much as a coffee mug and a doughnut share one hole. That rigidity makes them stable: edge states in the quantum Hall effect and topological insulators survive impurities that preserve the relevant symmetry. But the protection requires an energy gap in the bulk. If the gap closes, the topological invariant stops being well defined and the edge states were thought to vanish.
Critical points work the opposite way. At the boiling point of water or the Curie point where iron loses its magnetism, the gap closes completely, microscopic detail washes out and very different materials share the same critical exponents, a universality recognized by the 1982 Nobel Prize in Physics. One framework relies on a gap, the other on its absence, and for decades they developed largely apart.
Xue-Jia Yu of the Eastern Institute of Technology in Ningbo, a co-corresponding author on both papers who supplied the theory, was among the few theorists who asked whether topology could survive at a critical point. His group proposed a classification for topology at quantum critical points in 2022, a generalized bulk-edge correspondence for critical points in 2024, and an extension to nonequilibrium dynamics in 2026. With Limei Xu of Peking University and Hai-Qing Lin of Zhejiang University, he also wrote the first comprehensive review of the subject for Physics Reports.
Testing the idea was hard. Experimenters had to tune a system exactly to the critical point, where the bulk is fully gapless, and still pick out topological edge signals from strong fluctuations and noise. Yu's group likens it to stopping a fast train at a cliff edge while measuring a speck of dust on its wheel.
The two teams took different routes. In the first study, "Observation of critical topological phase transition," the experimenters saw topological zero-energy modes and so-called π modes at a one-dimensional Floquet critical point. In the second, "Experimental observation of critical topology," led by Zhi-Kang Lin and colleagues, the team used a generalized Li–Haldane bulk-edge correspondence and measured the entanglement spectrum to see critical topological behavior in both one and two dimensions.
Together the papers give the first experimental evidence in real physical systems that topology can survive when the energy gap closes, and that universal critical behavior and topological properties can coexist. The authors say the work opens possibilities for topological quantum computation, new acoustic devices and nonequilibrium topological phases. "Topology and criticality, two concepts once considered incompatible, have finally met in the laboratory," the Eastern Institute of Technology said in announcing the results.
