Is the quantum melting of a polaron Wigner Crystal an insulator-to-superconductor transition ?

On examining the stability of a Wigner Crystal (WC) in an ionic dielectric, two competitive effects due to Polaron formation are found to be important : (i) the screening of the Coulomb forces which destabilizes the crystal, c ompensated by (ii) the increase of the carrier mass (polaron mass). The qua ntum melting of the Polaron Wigner Crystal (PWC) is examined. By calculatin g the quantum fluctuations of both the electrons and the polarization, we s how that there is a competition between the dissociation of the Polarons at the insulator-to-metal transition (IMT), and a melting towards a polaron l iquid. We find that at strong coupling (alpha > alpha*), a liquid state of polarons cannot exist, and the IMT is driven by polaron dissociation. Next, we show that the dipolar interactions between localized polarons are respo nsible for a phonon instability of the PWC as the density increases. This p rovides a new mechanism for the IMT in doped dielectrics. Examining the sig n of the dielectric constant of the PWC, we conjecture that such an instabi lity could yield an Insulator-to-Superconductor transition.