  We present the results of two-fluid hydrodynamical simulations of
circumbinary discs consisting of gas and dust, with and without embedded
planets, to examine the influence of the dust on the structure of the tidally
truncated inner cavity and on the parking locations of migrating planets. In
this proof-of-concept study, we consider Kepler-16 and -34 analogues, and
examine dust fluids with Stokes numbers in the range $10^{-4} \le St \le
10^{-1}$ and dust-to-gas ratios of 0.01 and 1. For the canonical dust-to-gas
ratio of 0.01, we find the inclusion of the dust has only a minor effect on the
cavity and stopping locations of embedded planets compared to dust-free
simulations. However, for the enhanced dust-to-gas ratio of unity, assumed to
arise because of significant dust drift and accumulation, we find that the dust
can have a dramatic effect by shrinking and circularising the inner cavity,
which brings the parking locations of planets closer to the central binary.
This work demonstrates the importance of considering both gas and dust in
studies of circumbinary discs and planets, and provides a potential means of
explaining the orbital properties of circumbinary planets such as Kepler-34b,
which have hitherto been difficult to explain using gas-only hydrodynamical
simulations.
