Topological insulators and topological semimetals are both new classes of
quantum materials, which are characterized by surface states induced by the
topology of the bulk band structure. Topological Dirac or Weyl semimetals show
linear dispersion round nodes, termed the Dirac or Weyl points, as the
three-dimensional analogue of graphene. We review the basic concepts and
compare these topological states of matter from the materials perspective with
a special focus on Weyl semimetals. The TaAs family is the ideal materials
class to introduce the signatures of Weyl points in a pedagogical way, from
Fermi arcs to the chiral magneto-transport properties, followed by the hunting
for the type-II Weyl semimetals in WTe2, MoTe2 and related compounds. Many
materials are members of big families and topological properties can be tuned.
As one example, we introduce the multifuntional topological materials, Heusler
compounds, in which both topological insulators and magnetic Weyl semimetals
can be found. Instead of a comprehensive review, this article is expected to
serve as a helpful introduction and summary by taking a snapshot of the quickly
expanding field.Comment: 19 pages, 7 figures, an invited review article for Annual Review of
Condensed Matter Physic
