  Excitonic condensate has been long-sought within bulk indirect-gap
semiconductors, quantum wells, and 2D material layers, all tried as carrying
media. Here we propose intrinsically stable 2D semiconductor heterostructures
with doubly-indirect overlapping bands as optimal platforms for excitonic
condensation. After screening hundreds of 2D materials, we identify candidates
where spontaneous excitonic condensation mediated by purely electronic
interaction should occur, and hetero-pairs Sb2Te2Se/BiTeCl, Hf2N2I2/Zr2N2Cl2,
and LiAlTe2/BiTeI emerge promising. Unlike monolayers, where excitonic
condensation is hampered by Peierls instability, or other bilayers, where
doping by applied voltage is required, rendering them essentially
non-equilibrium systems, the chemically-specific heterostructures predicted
here are lattice-matched, show no detrimental electronic instability, and
display broken type-III gap, thus offering optimal carrier density without any
gate voltages, in true-equilibrium. Predicted materials can be used to access
different parts of electron-hole phase diagram, including BEC-BCS crossover,
enabling tantalizing applications in superfluid transport, Josephson-like
tunneling, and dissipationless charge counterflow.
