  The recent discovery of the first Weyl semimetal in TaAs provides the first
observation of a Weyl fermion in nature. Such a topological semimetal features
a novel type of anomalous surface state, the Fermi arc, which connects a pair
of Weyl nodes through the boundary of the crystal. Here, we present theoretical
calculations of the quasi-particle interference (QPI) patterns that arise from
the surface states including the topological Fermi arcs in the Weyl semimetals
TaAs and NbP. Most importantly, we discover that the QPI exhibits
termination-points that are fingerprints of the Weyl nodes in the interference
pattern. Our results, for the first time, propose an interference signature of
the topological Fermi arcs in TaAs, which provides important guidelines for STM
measurements on this prototypical Weyl semimetal compound. The scattering
channels presented here is relevant to transport phenomena on the surface of
the TaAs class of Weyl semimetals. Our work is also the first systematic
calculation of the quantum interferences from the Fermi arc surface states,
which is in general useful for future STM studies on other Weyl semimetals.
