Do topological electrons interact differently than normal electrons? We discuss three paths to answering this question.

One route is to engineer a new material with nontrivial topology and long-range magnetic order. In the first part of this dissertation we present a new material, YbMnSb2, and we provide evidence from transport, thermodynamic, and spectroscopic measurements to show that it is an antiferromagnetic topological semimetal. The majority of this work was published as Kealhofer, et al., Phys. Rev. B 97, 045109.

Another route to answer this question is to study the role of topology in strongly interacting systems. The cerium monopnictides CeSb and CeBi incorporate threads from f-electron magnetism, many-body (e.g. Kondo) physics, and topology. CeSb is a trivial semimetal, while CeBi is a topological semimetal. in the second part of this dissertation, we will untangle some of these threads and present our investigation of the relationship between topology, magnetism, and Kondo-like hybridization in CeSb and CeBi. The main tool we will use is angle-resolved photoemission spectroscopy (ARPES), taking advantage of the MERLIN beamline at the Advanced Light Source and its ability to resonantly tune to the Ce N-edge. This capability allows us to be exquisitely sensitive to the photoemission signal originating from the Ce f electrons. We will see that the signatures of magnetic interactions in CeSb and CeBi are markedly different, a difference whose origin may be the presence of topological band crossings in CeBi. Our work on CeSb was published as Jang, Kealhofer, et al., Sci. Adv. 5(3) eaat7158.

A third route to studying interactions in topological semimetals is to somehow reduce the dimension of the material from three to one. Fermi liquids abound in three dimensions--metals (and semimetals) are everywhere. In one dimension, though, the the ground state for a large number of interacting fermions is not the Fermi liquid but the Tomonaga-Luttinger liquid. So it would seem that if, in the laboratory, there were a knob labeled ``Dimension'' which one could turn from "3" to "1," it would be easy to study non-Fermi liquids.

In the final part of this dissertation, we discuss a future experiment which would attempt to turn this knob in TaAs, a Weyl semimetal. As one of the experimental consequences of the Fermi liquid is the proportionality of thermal conductivity and electrical conductivity at a fixed temperature (the Wiedemann-Franz law), the proposed experiment is to measure this ratio (the Lorenz number) in a strong applied magnetic field. Due to TaAs's low carrier density, at even relatively moderate fields of 5 T or lower the electrons will occupy only the lowest Landau level. As a result, conduction along the field direction is relatively unchanged, while the conduction perpendicular to the field is reduced, giving rise to a dimensional crossover. Measuring thermal conductivity through this crossover will allow us to observe signatures of the one dimensional conducting state, in which interactions between electrons cannot be ignored.