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