Identification of novel spin Hall platforms using magnetic flux tubes

Field theory arguments suggest the possibility of Z classification of quantum spin Hall effect with magnetic flux tubes, that cause separation of spin and charge degrees of freedom, and pumping of spin or Kramers pair. However, the proof of principle demonstration of spin-charge separation is yet to be accomplished for realistic, ab initio band structures of spin-orbit-coupled materials, lacking spin-conservation law. In this work, we perform thought experiments with magnetic flux tubes to unambiguously identify, for the first time, two-dimensional materials supporting unit and double strength spin Chern numbers from first-principles data. Our work sets a new standard for prediction of two-dimensional, quantum spin-Hall materials, based on precise bulk invariant and universal topological response.