Resonant Inelastic X-ray Spectroscopy on Electric Quadrupole Insulator

One of the guiding principles that experimentally capture a topological property is bulk-edge correspondence, and many studies focus on the edges by following the principle. In this study, we propose that a scattering experiment can capture the topological properties of materials which is essentially bulk property. As a representative example, we show that resonant inelastic X-ray spectroscopy on an electric quadrupole insulator. At specific energy and momentum transfer, we show that the scattering amplitude should vanish or not in a trivial or topological phase by symmetry arguments.