Global and local topological quantized responses from geometry, light, and time
Résumé
To describe a spin- particle on the Bloch sphere with a radial magnetic field and topological states of matter from the reciprocal space, we introduce square () as a local formulation of the global topological invariant. For the Haldane model on the honeycomb lattice, this can be measured from the Dirac points through circularly polarized light related to the high-symmetry point(s). For the quantum spin Hall effect and the Kane-Mele model, the topological number robust to interactions can be measured locally from a correspondence between the Pfaffian and light. We address a relation with a spin pump and the quantum spin Hall conductance. The analogy between light and magnetic nuclear resonance may be applied for imaging, among other applications.