Melting of a Wigner Crystal in an Ionic Dielectric

TL;DR

This paper investigates how a Wigner Crystal of electrons melts into a polaronic state within a polar host medium, analyzing the effects of density, temperature, and electron-phonon coupling on phase transitions and insulator-metal behavior.

Contribution

It introduces a detailed phase diagram for Wigner Crystal melting considering electron-phonon interactions and polaron dissociation, including effects of anisotropic band masses.

Findings

Critical density for melting estimated using Lindeman criterion.

Polaron dissociation prevents quantum liquid formation at high electron-phonon coupling.

Phase diagram shows insulator-to-metal transition driven by polaron ionization.

Abstract

The melting of a Wigner Crystal of electrons placed into a host polar material is examined as a function of the density and the temperature. When the coupling to the longitudinal optical modes of the host medium is turned on, the WC is progressively transformed into a polaronic Wigner Crystal. We estimate the critical density for crystal melting at zero temperature using the Lindeman criterion. We show that above a certain critical value of the Frohlich electron-phonon coupling, the melting towards a quantum liquid of polarons is not possible, and the insulator-to-metal transition is driven by the ionization of the polarons (polaron dissociation). The phase diagram at finite temperature is obtained by making use of the same Lindeman criterion. Results are also provided in the case of an anisotropic electron band mass, showing that the scenario of polaron dissociation can be relevant in anisotropic compounds such as the superconducting cuprates at rather moderate e-ph couplings.