The topological structure of the integral quantum Hall effect in magnetic semiconductor-superconductor hybrids

An unconventional integer quantum Hall regime was found in magnetic semiconductor-superconductor hybrids. By making use of the decomposition of the gauge potential on a U(1) principal fibre bundle over k-space, we study the topological structure of the integral Hall conductance. It is labeled by the Hopf index β and the Brouwer degree \eta. The Hall conductance topological current and its evolution is discussed.