Charge-density-waves and superconductivity as an alternative to phase separation in the infinite-U Hubbard-Holstein model

TL;DR

This paper explores how charge density waves and superconductivity emerge from the interplay of strong correlations, electron-phonon interactions, and Coulomb forces in the Hubbard-Holstein model, offering insights into cuprate physics.

Contribution

It provides a detailed analysis of density and Cooper instabilities considering long-range Coulomb effects and strong correlations, highlighting conditions for charge order and superconductivity.

Findings

Long-range Coulomb forces induce incommensurate charge density waves.

Charge instabilities can lead to superconductivity in strongly correlated systems.

Frustrated phase separation results in complex charge ordering phenomena.

Abstract

We investigate the density instabilities present in the infinite-U Hubbard-Holstein model both at zero and finite momenta as well as the occurrence of Cooper instabilities with a specific emphasis on the role of long-range Coulomb forces. In carrying out this analysis a special attention is devoted to the effects of the strong local $e$-$e$ interaction on the $e$-$ph$ coupling and particularly to both the static and dynamic screening processes dressing this coupling. We also clarify under which conditions in strongly correlated electron systems a weak additional interaction, e.g. a phonon-mediated attraction, can give rise to a charge instability. In the presence of long-range Coulomb forces, the frustrated phase separation leads to the formation of incommensurate charge density waves. These instabilities, in turn, lead to strong residual scattering processes between quasiparticles and to superconductivity, thus providing an interesting clue to the interpretation of the physics of the copper oxides.