Generic coexistence of Fermi arcs and Dirac cones on the surface of time-reversal invariant Weyl semimetals

The hallmark of Weyl semimetals is the existence of open constant-energy contours on their surface -- the so-called Fermi arcs -- connecting Weyl points. Here, we show that for time-reversal symmetric realizations of Weyl semimetals these Fermi arcs in many cases coexist with closed Fermi pockets originating from surface Dirac cones pinned to time-reversal invariant momenta. The existence of Fermi pockets is required for certain Fermi-arc connectivities due to additional restrictions imposed by the six $\mathbb{Z}_2$ topological invariants characterizing a generic time-reversal invariant Weyl semimetal. We show that a change of the Fermi-arc connectivity generally leads to a different topology of the surface Fermi surface, and identify the half-Heusler compound LaPtBi under in-plane compressive strain as a material that realizes this surface Lifshitz transition. We also discuss universal features of this coexistence in quasi-particle interference spectra.