Experimental perspective on three-dimensional topological semimetals

Topological semimetals (TSMs) are characterized by bulk band crossings in their electronic structures, which are expected to give rise to gapless electronic excitations and topological features that underlie exotic physical properties. The most famous examples are Dirac and Weyl semimetals, in which the corresponding low-energy fermionic excitations, i.e., the Dirac and Weyl fermions, are direct analogs of elementary particles in quantum field theory. The last decade has witnessed an explosion of research activities in the field of TSMs thanks to precise theoretical predictions, well-controlled material synthesis, and advanced characterization techniques including angle-resolved photoemission spectroscopy, scanning tunneling microscopy, magnetotransport measurements, optical spectroscopy, etc. Here recent progress in three-dimensional TSMs is reviewed with an emphasis on their characteristic bulk electronic structures, including dimensionality (such as zero-dimensional nodal points, one-dimensional nodal lines, and two-dimensional nodal surfaces), degeneracy (twofold, threefold, fourfold, sixfold, or eightfold) of the band crossing, the slope (type I and type II) and order (linear, quadratic, or cubic) of the band dispersion near the crossing, the characteristic topological invariants (such as monopole charges), and the crystallographic symmetries that stabilize the band crossings. The distinct signatures of the various topological semimetal phases, such as the nontrivial surface states (including Fermi arcs of Dirac and Weyl semimetals) and the unique transport and optical responses (such as chiral anomaly-induced negative magnetoresistance in Dirac and Weyl semimetals), are also reviewed.