  The surface of a Weyl semimetal famously hosts an exotic topological metal
that contains open Fermi arcs rather than closed Fermi surfaces. In this work,
we show that the surface is also endowed with a feature normally associated
with strongly interacting systems, namely, Luttinger arcs, defined as zeros of
the electron Green's function. The Luttinger arcs connect surface projections
of Weyl nodes of opposite chirality and form closed loops with the Fermi arcs
when the Weyl nodes are undoped. Upon doping, the ends of the Fermi and
Luttinger arcs separate and the intervening regions get filled by surface
projections of bulk Fermi surfaces. Remarkably, unlike Luttinger contours in
strongly interacting systems, the precise shape of the Luttinger arcs can be
determined experimentally by removing a surface layer. We use this principle to
sketch the Luttinger arcs for Co and Sn terminations in
Co$_{3}$Sn$_{2}$S$_{2}$. The area enclosed by the Fermi and Luttinger arcs
approximately equals the surface particle density in weakly coupled systems
while the correction is governed by the interlayer couplings and the perimeter
of the Fermi-Luttinger loop.

Strongly Correlated Electrons;Materials Science