[Physics] Chern number in condensed matter physics

condensed-matterdifferential-geometryquantum-hall-effecttopology

In mathematics, the Chern number is defined in terms of the Chern class of a manifold. What is the exact definition of Chern number in condensed matter physics, i.e. quantum hall system?

Best Answer

In quantum Hall effect(QAHE), Klitzing found the Hall conductivity to be integer multiples of a fundamental constant. This effect is independent of size and impurities of the system with which we deals with. Based on it, a famous scientist R. Laughlin proposed a theory describing the integer states in terms of a topological invariant. This topological invariant is known as chern number.

For details of the cern number,there is a wikipedia link.