Surface Luttinger arcs in Weyl Semimetals

Weyl semimetals – 3D topological materials in which non-degenerate conduction and valence bands cross at certain points in the Brillouin zone – have garnered attention in recent years. Despite the surface hosting Fermi arcs, fundamental sum-rules obeyed by general Fermi liquids, such as Luttinger’s theorem that equates particle density to the Fermi volume, are naïvely inapplicable to the surface metal since it lacks a closed Fermi surface. In this work, we show that the surface of a Weyl semimetal is endowed with another feature, the Luttinger arc, defined as the momentum space contour where the electron Green’s function vanishes. We show that the Luttinger arcs, like the Fermi arcs, also connect surface projections of Weyl nodes of opposite chirality. As a result, the Fermi and Luttinger arcs together form closed loops in undoped Weyl semimetals. Furthermore, we show that the closed loops fulfill Luttinger’s theorem in a physical limit and the equivalence obtained survives interactions if the system remains in the Weyl limit. Finally, we propose a direct method for detecting Luttinger arcs experimentally in bilayered Weyl semimetals and apply this  idea to determine Luttinger arcs in Co₃Sn₂S₂ using existing photoemission data.