Phonon Induced Instabilities in Correlated Electron Hamiltonians

TL;DR

This paper investigates how electron-phonon interactions influence phase stability in correlated electron systems, revealing competition between charge density waves and antiferromagnetic order, with implications for 2D materials.

Contribution

It extends the analysis of electron-phonon coupled Hamiltonians to quasi-two-dimensional systems using the functional renormalization group, highlighting phase competition and phonon effects.

Findings

Charge density wave and antiferromagnetic phases compete in the models.

Doping shifts the balance, leading to incommensurate order.

Charge ordering impacts phonon modes and quasiparticle weights.

Abstract

Studies of Hamiltonians modeling the coupling between electrons as well as to local phonon excitations have been fundamental in capturing the novel ordering seen in many quasi-one dimensional condensed matter systems. Extending studies of such Hamiltonians to quasi-two dimensional systems is of great current interest, as electron-phonon couplings are predicted to play a major role in the stabilization or enhancement of novel phases in 2D material systems. In this work, we study model systems that describe the interplay between the Hubbard coupling and the phonon modes in the Holstein (H) and Su-Schrieffer-Heeger (SSH) Hamiltonians using the functional renormalization group (fRG). For both types of electron phonon couplings, we find the predicted charge density wave phases in competition with anti-ferromagnetic ($AF$) ordering. As the system is doped, the transition shifts, with both orders showing incommensurate peaks. We compare the evolution of the quasiparticle weight for the Holstein model with that of the SSH model as the systems transition from antiferromagnetic to charge-ordered ground states. Finally, we calculate the self-energy of the phonon and capture the impact of charge ordering on the phonon modes.