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 ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$. 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.

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• Edge states
• Fermi surface
• Surface states
• Surfaces
• Weyl semimetal
• Green's function methods