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Topological foundations of ferroelectricity
The 21st century has witnessed a paradigm shift in material science, driven by the application of topological principles offering a global perspective on material properties beyond traditional local interactions. Ferroelectrics, known for their spontaneous polarization and technological significance, have now emerged as a rich platform for hosting fundamental topological states at the nanoscale. This Review explores the topological foundation of ferroelectricity, rooted in the electrostatic essence of these materials. Drawing upon the analogy between the hydrodynamics of incompressible fluids and the electrostatics of polarization fields, we establish a comprehensive framework for classifying the complex topological states observed in ferroelectrics. We demonstrate that the rich diversity of polarization structures can be exhaustively described using the advanced topological approach. By extending fundamental topological concepts such as helicity, fibration, foliation, and ergodicity, we offer a systematic analysis of the topological textures in ferroelectrics. This work provides a coherent framework for understanding and manipulating topological structures in nanostructured ferroelectrics, paving the way for innovations in materials science and technology.
