Bulk spectroscopic measurement of the topological charge of Weyl nodes with resonant x rays

We formulate a bulk spectroscopic method for direct measurement of the topological invariant of nondegenerate band crossings in Weyl semimetals. We demonstrate how polarization-resolved resonant x-ray scattering captures the winding of the Berry flux around Weyl nodes. The spectra obtained by the proposed strategy feature an integer number of zero crossings that is directly related to the topological charge of the measured nodes. We benchmark the proposed protocol on TaAs, using realistic low-energy models derived from density-functional theory to accurately represent the states close to the Fermi level, including sizable deviations from the idealized linear dispersion. We conclude that the proposed measurement, which is within the reach of current experimental setups, yields direct signatures of nontrivial band topology in the spectroscopy of three-dimensional bulk matter.