topological phase transitions

Topological phase transitions are changes between different states of matter that involve the material's microscopic structure and properties rather than just temperature or pressure. In these transitions, the material shifts from one phase to another with distinct "topological" features—like how certain properties are preserved even if the material is deformed. This is similar to swapping one kind of surface shape for another, where the overall connectivity or “twist” remains fundamentally different. These transitions often lead to novel behaviors, such as conducting electricity along edges without loss, and are key to developing advanced electronic technologies.