  We examine the response of the Fermi arc in the context of quasi-particle
interference (QPI) with regard to a localized surface impurity on various
three-dimensional Weyl semimetals (WSMs). Our study also reveals the variation
of the local density of states (LDOS), obtained by Fourier transforming the QPI
profile, on the two-dimensional surface. We use the $T$-matrix formalism to
numerically (analytically and numerically) capture the details of the momentum
space scattering in QPI (real space decay in LDOS), considering relevant
tight-binding lattice and/or low-energy continuum models modeling a range of
different WSMs. In particular, we consider multi-WSM (mWSM), hosting multiple
Fermi arcs between two opposite chirality Weyl nodes (WNs), where we find a
universal $1/r$-decay ($r$ measuring the radial distance from the impurity
core) of the impurity-induced LDOS, irrespective of the topological charge.
Interestingly, the inter-Fermi arc scattering is only present for triple WSMs,
where we find an additional $1/r^3$-decay as compared to double and single
WSMs. The untilted single (double) [triple] WSM shows a straight-line
(leaf-like) [oval-shaped] QPI profile. The above QPI profiles are canted for
hybrid WSMs where type-I and type-II Weyl nodes coexist, however, hybrid single
WSM demonstrates strong non-uniformity, unlike the hybrid double and triple
WSMs. We also show that the chirality and the positions of the Weyl nodes
imprint marked signatures in the QPI profile. This allows us to distinguish
between different WSMs, including the time-reversal-broken WSMs from the
time-reversal-invariant WSM, even though both of the WSMs can host two pairs of
Weyl nodes. Our study can thus shed light on experimentally obtainable complex
QPI profiles and help differentiate different WSMs and their surface band
structures.
