  The possibility of inter-layer exciton condensation in a holographic
D3-probe-D5 brane model of a strongly coupled double monolayer Dirac semi-metal
in a magnetic field is studied in detail. It is found that, when the charge
densities on the layers are exactly balanced so that, at weak coupling, the
Fermi surfaces of electrons in one monolayer and holes in the other monolayer
would be perfectly nested, inter-layer condensates can form for any separation
of the layers. The case where both monolayers are charge neutral is special.
There, the inter-layer condensate occurs only for small separations and is
replaced by an intra-layer exciton condensate at larger separations. The phase
diagram for charge balanced monolayers for a range layer separations and
chemical potentials is found. We also show that, in semi-metals with multiple
species of massless fermions, the balance of charges required for Fermi surface
nesting can occur spontaneously by breaking some of the internal symmetry of
the monolayers. This could have important consequences for experimental
attempts to find inter-layer condensates.
