MATHEMATICAL SCIENCES

The Nankai team has made a new breakthrough in the study of symmetry protection topology in subspace


Topology is a branch of mathematics that studies the geometric properties of objects, but in physics, the concept of topology can be used to describe the band characteristics of matter, so as to study novel topological states and various new topological materials. The most typical feature of nontrivial topology is that there is a topological boundary state protected by a specific symmetry, so that it is generally considered that the topological boundary state, topological invariant and symmetry are closely related and indispensable, that is, any perturbation that breaks the symmetry will destroy the topological invariant and the topological boundary state at the same time.

Recently, the research of Chen Zhigang, a professor at the School of Physics of Nankai University/TEDA Institute of Applied Physics, and foreign scholars has challenged this traditional concept. They found that even if the system no longer has quantized topological invariants and some kind of overall symmetry, topological boundary states can still exist in the corresponding subspace, protected by subsymmetry. The research was published in Nature Physics.

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Schematic diagram of the classification of perturbations in the SPT phase of symmetry protection. The yellow line region represents a set of perturbations that satisfy a specific symmetry and do not break the topological invariant of the overall system (Topo.Invariant). Each boundary state is protected by its associated subsymmetry (SubSy), where the red and blue line regions represent two sets of perturbations satisfying subsymmetry, respectively, where the perturbations destroy the topological invariants of the overall system, but do not affect the boundary states protected by subsymmetry; Overlapping regions represent topological invariants and corresponding topological boundary states when the topology is identical.  Photo courtesy of Nankai University

By introducing and exploring the concept of sub-symmetry, researchers find that global symmetry in the traditional sense is not completely necessary for the protection of topological boundary states. In fact, the topological boundary state is protected as long as the symmetry of a particular subspace is satisfied, even if the overall topological invariant no longer exists.

The research team cleverly designed and prepared the photonic lattice structure by using low-light direct writing to meet the symmetry conditions of different subspaces, and experimentally demonstrated the topological states protected by subsymmetry in the most typical one-dimensional SSH and two-dimensional Kagome topological lattices. In addition, they innovatively introduced long-range coupled symmetry in the Kagome lattice model, which solved the current controversy about the existence and topological protection of higher-order topological states in the Kagome lattice.

It is reported that this study not only challenges people’s traditional understanding of symmetry-protected topological states, but also provides new ideas for the research and application of topological states in different physical contexts. This achievement is expected to further promote the development of topological photonics and its frontier intersection and the research and development of a new generation of topological photonic devices. (Source: China Science News, Dai Jianfang, Chen Bin)

Related paper information: https://doi.org/10.1038/s41567-023-02011-9



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