  The topological nature of Weyl semimetals (WSMs) is corroborated by the
presence of chiral surface states, which connect the projections of the bulk
Weyl points by Fermi arcs (FAs). We study a bilayer structure realized by
introducing a thin insulating spacer into a bulk WSM. Employing a
self-consistent mean-field description of the interlayer Coulomb interaction,
we propose that this system can develop an interlayer electron-hole pair
condensate. The formation of this excitonic condensate leads to partial gapping
of the FA dispersion. We obtain the dependence of the energy gap and the
critical temperature on the model parameters, finding, in particular, a linear
scaling of these quantities with the separation between the Weyl points in
momentum space. A detrimental role is played by the curvature of the FAs,
although the pairing persists for moderately small curvature. A signature of
the condensate is the modification of the quantum oscillations involving the
surface FAs.
