  The Weyl semimetal phase is a recently discovered topological quantum state
of matter characterized by the presence of topologically protected degeneracies
near the Fermi level. These degeneracies are the source of exotic phenomena,
including the realization of chiral Weyl fermions as quasiparticles in the bulk
and the formation of Fermi arc states on the surfaces. Here, we demonstrate
that these two key signatures show distinct evolutions with the bulk band
topology by performing angle-resolved photoemission spectroscopy, supported by
first-principle calculations, on transition-metal monophosphides. While Weyl
fermion quasiparticles exist only when the chemical potential is located
between two saddle points of the Weyl cone features, the Fermi arc states
extend in a larger energy scale and are robust across the bulk Lifshitz
transitions associated with the recombination of two non-trivial Fermi surfaces
enclosing one Weyl point into a single trivial Fermi surface enclosing two Weyl
points of opposite chirality. Therefore, in some systems (e.g. NbP),
topological Fermi arc states are preserved even if Weyl fermion quasiparticles
are absent in the bulk. Our findings not only provide insight into the
relationship between the exotic physical phenomena and the intrinsic bulk band
topology in Weyl semimetals, but also resolve the apparent puzzle of the
different magneto-transport properties observed in TaAs, TaP and NbP, where the
Fermi arc states are similar.
