Competing orders at the interface of a bilayer Weyl system with Fermi arcs*

We study interaction effects at the interface of two Weyl semimetals, each with multiple Fermi arc states on their surfaces. We consider competing spontaneous orderings in the ground-state, in particular charge density and inter-surface exciton condensation. The resulting phases offer rich physics which can depend strongly on the relative orientation of the Fermi arcs.