An Overview of the Development of Topological Vortex Theory (TVT) |...

An Overview of the Development of Topological Vortex Theory (TVT)

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2. The Key Developmental Stages of Topological Vortex Theory (TVT)

The development of Topological Vortex Theory (TVT) can be traced back to the study of topological phase transitions in condensed matter physics during the 1970s, and it gradually evolved into an interdisciplinary theoretical framework in the 21st century. The following are its key developmental stages:

2.1 Theoretical Emergence: BKT Transition and Topological Defects

In the 1970s, Thouless and Kosterlitz proposed the BKT transition theory by studying vortex-antivortex bound pairs in two-dimensional superfluid/superconducting systems. This theory revealed the role of topological defects (such as vortices) in phase transitions, breaking through the limitations of the Landau paradigm and laying the foundation for subsequent topological classification.

2.2 Mathematical Deepening: Chern Number and Quantum Hall Effect

In the 1980s, Thouless and his students introduced the Chern number to quantify the topological properties of electron wavefunctions, explaining the microscopic mechanism of the quantum Hall effect. Haldane further proposed the quantum anomalous Hall effect, integrating topological classification with symmetry constraints and advancing the study of topological insulators.

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