Machine learning is revolutionizing fundamental science by tackling long-standing mathematical challenges. A key example is the classification of topological phases of matter. While topological invariants have been essential for characterizing these phases, no single invariant works universally. This limitation has led to many phases, once considered trivial, being reclassified as topological over the years. The recent discovery of non-Hermitian band topology has intensified efforts to classify these new phases, yet existing invariants still fail to capture all their unique features. Now, researchers from Tongji University, the Chinese university of Hong Kong and Nanyang Technological University have developed a machine-learning algorithm that performs unsupervised classification of symmetry-protected non-Hermitian topological phases—without relying on any predefined topological invariants. The method can autonomously construct a topological periodic table, bypassing the need for advanced mathematics. The learning process also yielded a formula revealing how parity transformation affects periodicity. Additionally, the algorithm accounts for boundary effects, allowing investigation of how open boundaries influence the topological phase diagram. These findings establish a powerful unsupervised framework for identifying non-Hermitian topological phases, uncover previously hidden topological traits, and offer valuable insights for future theoretical and experimental work.

The research group of Professor Chuandong Dou at the State Key Laboratory of Supramolecular Structure and Materials, Jilin University, recently constructed two novel boron-hexane two-dimensional benzobenzenes using a borane-controlled cyclization strategy, elucidating the importance of boron atom doping. Using conjugated boranes as precursors, the researchers synthesized boron-hexane Z-type and bilayer benzobenzenes C₃₂B₂ via FeCl₃ and Bi(OTf)₃-mediated intramolecular cyclization reactions, obtaining narrow-spectrum fluorescence (half-width at half-maximum as narrow as 19 nm) and amplified spontaneous emission properties, demonstrating their potential application as gain mediators. Furthermore, by studying the electronic structures of their divalent anions and all-carbon isoelectronic forms, they revealed that boron atoms can perturb the aromaticity of the conjugated framework, thereby reconstructing the spin density distribution. This research expands the topological diversity of boron-containing carbon molecules and provides a new system for studying luminescent functions and spin properties. The article was published as an open access Research Article in CCS Chemistry, the flagship journal of the Chinese Chemical Society.