In collaboration with researchers from Nanyang Technological University in Singapore, Professor Jiang Jianhua and his team members at Suzhou Institute for Advanced Research, University of Science and Technology of China, reviewed the rapidly developing topological physics underpinning the generation of topological defects, and prospected its potential impacts on condensed matter physics, optics, acoustics and materials science. This review was recently published in the Nature Reviews Physics as the cover article under the title "Topological phenomena at defects in acoustic, photonic and solid-state lattices".

Topology has been applied into two prominent fields of materials physics, the currently circulating topological band theory used to predict and classify topological materials, and the real-space topology of defects that have been studied earlier, such as dislocations and disclinations. They are usually treated separately, but recent theoretical and experimental studies have demonstrated their complex and surprising interactions in solid materials and metamaterials. For instance, topological defects lead to various novel physical phenomena in topological materials, like robust topological localized states, fractional charges, topological Vanier cycles, chiral and gravitational anomalies, defect-induced pumping and non-Hermitian skin effects (as shown in Figure 1).

Figure 1 Typical topological defects and the resulting topological physical phenomena. a, b: Dirac vortices and Majorana-like localized States; c, d: screw dislocations and one-dimensional helical localized states; and e, f: disclination and fractional charge.

At the beginning of this review was a theoretical introduction to the one-dimensional Jackiw-Rebbi model and the two-dimensional Jackiw-Rossi theory. Then bulk-defect correspondence cases in different topological insulator systems were illustrated as weak topological insulator, three-dimensional integer quantum Hall system and two-dimensional Chern insulator according to Kane-Teo symmetry. This was followed by a physical mechanism of topological defect states. Subsequently, the author summarized a diverse range of novel phenomena of topological defects in different topological materials from topological insulators to topological crystalline insulators, topological semimetals, topological superfluidity, superconductivity, and strongly correlated systems. Also, recent experimental breakthroughs in solid materials and superstructure materials were reviewed, including one-dimensional topological localized states induced by screw dislocations in phononic and photonic systems, experimental measurement of fractional charges induced by disclinations in photonic and circuit systems, and the acoustic topological Vanier cycle.

The paper ended with an outlook of this field. Superstructural materials can continue to provide a medium for exploring the interaction of topological defects and other novel degrees of freedom, resulting in more interesting physics in artificial high-dimensional, non-Hermitian, non-Euclidean, nonlinear and other systems. In addition, topological defect states were expected to provide new applications and new ideas for new waveguides, high Q optical cavities, and high performance lasers. Nevertheless, how the abundant topological defect structures in solid nanomaterials affect the properties of topological materials and whether more applications can be found remains to be explored.

Table 1 Topological phenomena generated by different topological defects in different topological materials

Lin Zhikang, a doctoral student at School of Physical Science and Technology, Soochow University, is the first author of the paper, with NTU Professors Baile Zhang, Yidong Chong, and SIAR Professor Jiang Jianhua as the co-corresponding authors. Other collaborators include NTU Qiang Wang, Dr. Haoran Xue, and Liu Yang, a PhD student at Soochow University. The research was sponsored by the National Natural Science Foundation of China for Distinguished Young Scholars. The cover picture of the paper was created by Professor Wang Guoyan and Ma Yanbing, School of Communication, Soochow University.

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