Competition between excitonic charge and spin density waves: Influence of electron-phonon and Hund's rule couplings

TL;DR

This paper investigates how electron-phonon and Hund's rule interactions influence the stability and competition of excitonic charge and spin density waves in a two-band Hubbard model, revealing conditions favoring each phase.

Contribution

It introduces a combined mean-field and variational cluster approach to analyze the interplay of interactions in excitonic states, highlighting the conditions for charge versus spin density wave dominance.

Findings

Electron-phonon interaction stabilizes charge density waves.

Hund's rule coupling favors spin density waves.

Transition conditions between charge and spin density waves identified.

Abstract

We analyze the stability of excitonic ground states in the two-band Hubbard model with additional electron-phonon and Hund's rule couplings using a combination of mean-field and variational cluster approaches. We show that both the interband Coulomb interaction and the electron-phonon interaction will cooperatively stabilize a charge density wave (CDW) state which typifies an "excitonic" CDW if predominantly triggered by the effective interorbital electron-hole attraction or a "phononic" CDW if mostly caused by the coupling to the lattice degrees of freedom. By contrast, the Hund's rule coupling promotes an excitonic spin density wave. We determine the transition between excitonic charge and spin density waves and comment on a fixation of the phase of the excitonic order parameter that would prevent the formation of a superfluid condensate of excitons. The implications for exciton condensation in several material classes with strongly correlated electrons are discussed.