Polaron Crystallization and Melting: Effects of the Long-range Coulomb Forces

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 1/εsr, 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.