Instability due to long range Coulomb interaction in a liquid of polarizable particles (polarons, etc.)

TL;DR

This paper derives the interaction Hamiltonian for polarons with long-range Coulomb forces, predicts a liquid instability leading to metallization, and analyzes experimental differences between cuprates and nickelates.

Contribution

It introduces a mean-field dielectric function for polarons with Coulomb interaction and links the instability to optical mode softening and metallization.

Findings

Liquid of polarons becomes unstable at high concentration.

Optical mode softening signals the onset of instability.

Doped cuprates metallize, nickelates do not, explained by the theory.

Abstract

The interaction Hamiltonian for a system of polarons a la Feynman in the presence of long range Coulomb interaction is derived and the dielectric function is computed in mean field. For large enough concentration a liquid of such particles becomes unstable. The onset of the instability is signaled by the softening of a collective optical mode in which all electrons oscillate in phase in their respective self-trapping potential. We associate the instability with a metallization of the system. Optical experiments in slightly doped cuprates and doped nickelates are analyzed within this theory. We discuss why doped cuprates matallize whereas nickelates do not.