Topological contribution to magnetism in the Kane-Mele model: An explicit wave-function approach

In our previous publication [Ozaki and Ogata, Phys. Rev. Res. 3, 013058 (2021)], the quantization of orbital-Zeeman (OZ) cross term in magnetic susceptibility, or spin Zeeman orbital effect, was shown for Kane-Mele model using expansion around Dirac points. present study, we accurately evaluate orbital, spin-Zeeman, OZ a recently developed formulation. This method uses explicit real-space Bloch wave functions enables us to each contribution taking into account an infinite number high-energy bands core electron at arbitrary chemical potential. We find that effect beyond formulations does not change term. also study metalic case, sum rule with respect potential is found. The possibility experimental detection discussed.