  On examining the stability of a Wigner crystal in an ionic dielectric, two
competitive effects due to the polaron formation are found to be important: (i)
the screening of the Coulomb force, which destabilizes the crystal, compensated
by (ii) the increase of the carrier mass (polaron mass). The competition
between the two effects is carefully studied, and the quantum melting of the
polaronic Wigner crystal is examined by varying the density at zero
temperature. By calculating the quantum fluctuations of both the electron and
the polarization, we show that there is a competition between the dissociation
of the polarons at the insulator-to-metal transition (IMT), and a melting
towards a polaron liquid. We find that at strong coupling, a liquid state of
dielectric polarons cannot exist, and the IMT is driven by the polaron
dissociation. Next, taking into account the dipolar interactions between
localized carriers, we show that these are responsible for an instability of
the transverse vibrational modes of the polaronic Wigner crystal as the density
increases. This provides a new mechanism for the IMT in doped dielectrics,
which yields interesting dielectric properties below and beyond the transition.
An optical signature of such a mechanism for the IMT is provided.
