Charge instabilities in strongly correlated bilayer systems

TL;DR

This paper studies how charge instabilities in strongly correlated bilayer systems are influenced by short-range correlations, long-range Coulomb interactions, and electron-phonon coupling, with implications for high-Tc cuprates.

Contribution

It provides a detailed analysis of charge instabilities in the Hubbard-Holstein bilayer model, highlighting the roles of correlations and Coulomb interactions in charge-density wave formation.

Findings

Short-range correlations suppress finite wave-vector nesting instabilities.

Long-range Coulomb interactions frustrate q=0 instabilities and promote incommensurate CDWs.

CDW instability first appears in the antisymmetric channel at low doping.

Abstract

We investigate the charge-instabilities of the Hubbard-Holstein model with two coupled layers. In this system the scattering processes naturally separate into contributions which are either symmetric or antisymmetric combinations with respect to exchange of the layers. It turns out that the short-range strong correlations suppress finite wave-vector nesting instabilities for both symmetries but favor the occurrence of phase separation in the symmetric channel. Inclusion of a sizeable long-range Coulomb (LRC) interaction frustrates the q=0 instabilities and supports the formation of incommensurate charge-density waves (CDW). Upon reducing doping from half-filling and for small electron-phonon coupling g the CDW instability first occurs in the antisymmetric channel but both instability lines merge with increasing g. While LRC forces always suppress the phase separation instability in the symmetric channel, the CDW period in the antisymmetric sector tends to infinity (q_c -> 0) for sufficiently small Coulomb interaction. This feature allows for the possibility of singular scattering over the whole Fermi surface. We discuss possible implications of our results for the bilayer high-Tc cuprates.