Recent discovery of topological electronic states has shed light on the role of strong spin-orbit coupling in condensed mater. When the coupling is combined with electron correlation effect, their combination leads to a new class of topological states accompanying exotic magnetism. The 5d transition metal iridates have received considerable attention as the candidates that harness Kitaev quantum spin liquid, Wyle semimetal or Axion insulator phases. For the first part of this talk, I discuss resonant inelastic x-ray scattering (RIXS) investigation of a honeycomb Na2IrO3. The observation of diffuse magnetic scattering points to presence of short-range magnetic orders resulting from competition of bond-directional magnetic anisotropies. This validates the novel route to realize Kitaev spin liquid and evidences the proximity to the spin liquid phase. In the second part, I present RIXS study of magnetic excitation in a pyrochlore Eu2Ir2O7. Its metal-insulator transition driven by all-in-all-out (AIAO) magnetic order is regarded as possible realization of topological Weyl semimetal. We observe gradual softening of the magnon excitations in the entire Brillouin zone while warming, whose temperature evolution shows a direct relationship with the metal-insulator transition. This result suggests substantial change of magnetic exchange due to the varying electronic structure, and thereby classifies intermediate electron correlation strength: a requisite for realizing Weyl semimetal state.

The field of charged impurities in narrow-band gap semiconductors and Weyl semimetals can create electron-hole pairs when the total charge Ze of the impurity exceeds a value Z_{c}e.  Particles of one charge escape to infinity, leaving a screening space charge.  The result is that the observable dimensionless impurity charge Q_{infinity} is less than Z but greater than Z_{c}.  There is a corresponding effect for nuclei with Z >Z_{c} \approx 170, however in the condensed matter setting we find Z_{c} to be about 10.  Thomas-Fermi theory indicates that Q_{\infinity} = 0 for the Weyl semimetal, but we argue that this is a defect of the theory. For the case of a highly-charged recombination center in a narrow band-gap semiconductor (or of a supercharged nucleus),  the observable charge takes on a nearly universal value.  In Weyl semimetals the observable charge takes on the universal value Q_{infinity} = Z_{c} set by the reciprocal of material's fine structure constant.

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