  Ideal Weyl semimetals with all Weyl nodes exactly at the Fermi level and no
coexisting trivial Fermi surfaces in the bulk, similar to graphene, could
feature deep physics such as exotic transport phenomena induced by the chiral
anomaly. Here, we show that HgTe and half-Heusler compounds, under a broad
range of in-plane compressive strain, could be materials in nature realizing
ideal Weyl semimetals with four pairs of Weyl nodes and topological surface
Fermi arcs. Generically, we find that the HgTe-class materials with nontrivial
band inversion and noncentrosymmetry provide a promising arena to realize ideal
Weyl semimetals. Such ideal Weyl semimetals could further provide a unique
platform to study emergent phenomena such as the interplay between ideal Weyl
fermions and superconductivity in the half-Heusler compound LaPtBi.
