Search for topological semimetal and topological superconductor candidates

The discoveries of the two-dimensional quantum Hall effect, the quantum spin Hall effect, and three-dimensional topological insulators started a new era in solid-state physics. Topology soon became a word in most solid-state physicists' vocabulary. A topological phase of matter is characterized by a nonzero topological invariant, which is determined by the bulk electronic wavefunctions of a material. The conventional insulators and metals have a zero, or trivial, topological invariant, and their properties are not affected by the topology of their band structure. Topologically non-trivial materials, however, display a host of exotic phenomena in their transport and spectroscopic properties, and band topology has to be invoked to explain them.Band topology has even emerged as a classification principle of the states of matter, with the topological invariant characterizing the topological class of the materials. Soon after the discovery of topological insulators, topological semimetals were theoretically predicted and experimentally realized. These are gapless systems characterized by protected band crossings with linear energy dispersions resembling those of relativistic particles. The physical realization of these systems is important not only because of the opportunity to study novel quantum phases of matter and emergent phenomena which have led to the discoveries of surface Dirac cones, surface Fermi arcs, the chiral anomaly and colossal photovoltaic effects, but also because they hold promise for applications in quantum devices.Although it has recently been realized that topological materials are fairly ubiquitous in nature, signatures of their nontrivial topology are still not easily accessible due to the lack of ideal material realizations. For years this was the main obstacle in the study of nodal-line semimetals. For topological physics to be accessible, two things must occur. First, the nodes (line or point) must be very close to the Fermi level and second, there should be no other trivial bands at the Fermi level. The search for material realizations of ideal semimetals of each type is the subject of my dissertation.An ideal nodal-line semimetal predicted to satisfy both of these criteria is CaAgAs. We are the first group to synthesize single crystals of this material, and study their transport properties and band structure. We additionally studied CaCdGe, a compound with the same crystal structure and topological nodal line, but a much more complicated Fermi surface with trivial bands near the Fermi level. By comparing the transport properties of these two materials, our study provided evidence that the large magnetoresistance and the highly debated linear magnetoresistance seen in topological semimetals might simply be due to electron-hole compensation and charge fluctuations, respectively. Furthermore, a topological surface state was observed in our CaAgAs in our collaborative angle-resolved photoemission spectroscopy experiment, unambiguously proving that this material was correctly dubbed the "hydrogen atom" of nodal-line semimetals.Experimental work provides key insights that lead to a revision of the theory and thus our understanding of the physics of a material. This is what our study on CuMnAs accomplished. CuMnAs was predicted to be an antiferromagnetic Dirac semimetal, with a topological protection that relied on a theoretically predicted magnetic structure. However, no such structure had ever been experimentally confirmed. In our study, we grew single crystals of CuMnAs, resolved this magnetic structure and showed that it was actually different from the theoretically predicted one. Although this led to the Dirac fermions no longer being protected, our collaborative first-principles calculations found that it leads to the emergence of spin-polarized surface states, a much sought after property for spintronics. Many of the topological semimetals that are currently being studied were first synthesized decades ago. However, in light of new predictions regarding the topology of their band structure, their properties are now being re-examined. Our studies of NbGe2, a chiral non-centrosymmetric superconductor first studied in the 1970s and recently predicted to host Kramers-Weyl fermions, reveal that it might be possible for this material to harbor a superconducting topological surface state