  The recent experimental discovery of a Weyl semimetal in TaAs provides the
first observation of a Weyl fermion in nature and demonstrates a novel type of
anomalous surface state band structure, consisting of Fermi arcs. So far, work
has focused on Weyl semimetals with strong spin-orbit coupling (SOC). However,
Weyl semimetals with weak SOC may allow tunable spin-splitting for device
applications and may exhibit a crossover to a spinless topological phase, such
as a Dirac line semimetal in the case of spinless TaAs. NbP, isostructural to
TaAs, may realize the first Weyl semimetal in the limit of weak SOC. Here we
study the surface states of NbP by angle-resolved photoemission spectroscopy
(ARPES) and we find that we $\textit{cannot}$ show Fermi arcs based on our
experimental data alone. We present an $\textit{ab initio}$ calculation of the
surface states of NbP and we find that the Weyl points are too close and the
Fermi level is too low to show Fermi arcs either by (1) directly measuring an
arc or (2) counting chiralities of edge modes on a closed path. Nonetheless,
the excellent agreement between our experimental data and numerical
calculations suggests that NbP is a Weyl semimetal, consistent with TaAs, and
that we observe trivial surface states which evolve continuously from the
topological Fermi arcs above the Fermi level. Based on these results, we
propose a slightly different criterion for a Fermi arc which, unlike (1) and
(2) above, does not require us to resolve Weyl points or the spin splitting of
surface states. We propose that raising the Fermi level by $> 20$ meV would
make it possible to observe a Fermi arc using this criterion in NbP. Our work
offers insight into Weyl semimetals with weak spin-orbit coupling, as well as
the crossover from the spinful topological Weyl semimetal to the spinless
topological Dirac line semimetal.
