  We study a mixture of a dipolar condensate and a degenerate Fermi gas in a
quasi-one-dimensional geometry. We demonstrate that the presence of fermions
may drastically change the behavior of a dipolar condensate. For strong enough
boson-fermion attraction a dipolar Bose-Fermi droplet appears in the mixture
and a roton excitation develops in the Bogoliubov excitations spectrum. As
shown analytically and by solving numerically the coupled set of extended
Gross-Pitaevski and Hartree-Fock equations for bosonic and fermionic
components, respectively, roton instability mechanism leads to the formation of
supersolid phase in a Bose-Einstein condensate. Scaling arguments show that
although the dysprosium atoms are considered to demonstrate the appearance of
the supersolid phase, such a phase can be observed with less magnetic atoms
like chromium and even rubidium.
