Abstract：Superconductors, spin liquids, and topological semimetals are typical In this talk, I will present two of our recent studies where we have used scattering methods with neutrons and resonant X-rays as probing particles. By performing pixel-power-enabled mapping-styled measurements, which provide data coverage in the three-dimensional reciprocal space plus an extra dimension in energy or real time, we have obtained unprecedented insights into magnetically and charge-ordered systems.

In the first study, we establish the existence of magnon topological “semimetal” bands (with Dirac points) in a spin-1/2 antiferromagnet, Cu₃TeO₆, which turns out to be surprisingly “classical” in its magnetism because of long-range exchange interactions. The demonstrated topological band structure is new to the zoo of band topology.

In the second study, we take a very close look at the birth of charge density waves (CDW) in a prototypical Peierls CDW material, ZrTe₃. We demonstrate a new and rigorous route to differentiate incipient CDW against electronic standing waves, also known as Friedel oscillations (FO). Our result reveals that the CDW formation is actually promoted by self-amplifying FO, and it brings new insights to related phenomena in cuprate high-Tc superconductors.