Coexistence of Fermi arcs with two dimensional gapless Dirac states

We present a physical scenario in which both Fermi arcs and two-dimensional gapless Dirac states coexist as boundary modes at the same two-dimensional surface. This situation is realized in topological insulator-Weyl semimetal interfaces in spite of explicit time reversal symmetry breaking. Based on a heuristic topological index, we predict that the coexistence is allowed when (i) the corresponding states of the Weyl semimetal and topological insulator occur at disconnected parts of the Brillouin zone separated by the Weyl nodes and (ii) the time-reversal breaking vector defining the Weyl semimetal has no projection parallel to the domain wall. This is corroborated by a numerical simulation of a tight binding model. We further calculate the optical conductivity of the coexisting interface states, which can be used to identify them through interference experiments.