Chern number

The Chern number is a mathematical property that describes the global geometric characteristics of certain materials, particularly in the field of condensed matter physics. It quantifies how electronic states in a material “twist” or “wrap around” in a complex, multi-dimensional space called momentum space. This number is an integer that remains stable against small changes, providing a robust way to distinguish different phases of matter. In practical terms, a non-zero Chern number indicates the material can support special conducting states at its edges—crucial for understanding phenomena like the quantum Hall effect and designing advanced electronic devices.