Abstract
A confluence of precise theoretical predictions shows that carefully fabricated three-dimensional (3D) semimetals can host a variety of exotic phases dominated by topological constraints. This experimental review of 3D topological semimetals addresses the role that electronic structure and associated band crossings play in validating Dirac and Weyl fermion descriptions that have analogies with elementary particles in quantum field theory. The importance of Fermi arcs, nodal geometries, symmetry, spin-orbit coupling, and dimensionality is highlighted. A list of confirmed 3D topological semimetals is presented with suggestions for future research and applications.
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