We consider interaction-induced broken symmetry states of two Weyl semimetal surfaces with multiple Fermi-arc (FA) states. In the presence of inter- and intrasurface Coulomb interactions, multiple broken symmetries may emerge which coexist and/or compete with one another. Interlayer exciton condensates involving different FA flavors are shown to form, with amplitudes determined by the strength of interactions and the degree of nesting among the arcs. For FA pairs which are well separated in momentum with strong nesting, the resulting state is a particle-hole analog of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductor. Intralayer interactions moreover induce charge density wave (CDW) ordering, so that the most general state of the system is a supersolid. These orderings in principle carry signatures in nonlinear behavior and narrow band noise in Coulomb drag transport measurements.

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• Charge density waves
• Excitons
• Weyl semimetal
• Green's function methods