UC Davis

In recent years, the number of materials known to host symmetry--protected topological phases has grown dramatically. Although they were once considered exotic, it is now known that these kinds of sytems are relatively common, and methods have been developed to automatically discover and confirm these phases in non-interacting materials. Nevertheless, the interplay of strong correlations and topology remains largely unexplored, and it is expected that this regime hosts a plethora of exotic phases which are not adiabatically connected to those known for non-interacting systems. This dissertation focuses on a number of specific examples in this regime exploring the effect of topology in the context of heavy--fermion physics, metal--insulator transitions, and superconductivity. For the class of cerium--based heavy--fermion superconductors, the topological nodal lines in the normal state are used to explain the pairing symmetry of the superconducting state. In UNiSn, an inverted metal--insulator transition is shown to be a Weyl metal--topological insulator transition. The anomalous transport properties that arise in topological semimetals are also discussed in the context of UCo$_{0.8}$Ru$_{0.2}$Al, in which a collosal Nernst coefficient was recently measured. Finally, calculated exchange interactions for the recently discovered superconductor Nd$_{0.8}$Sr$_{0.2}$NiO$_{2}$ are discussed and compared to the isostructural cuprate superconductors.