Phonon dispersion and the competition between pairing and charge order

TL;DR

This study uses Quantum Monte Carlo simulations to explore how phonon dispersion influences superconducting and charge density wave phases in the Holstein Model, revealing competition between charge patterns and conditions favoring superconductivity.

Contribution

It provides new insights into the effects of phonon dispersion on phase competition and order in the Holstein Model, extending understanding beyond local phonon interactions.

Findings

Finite phonon bandwidth affects critical temperature for charge order.

Competition observed between different charge density wave patterns.

Superconductivity can emerge when phonon bandwidth suppresses charge order.

Abstract

The Holstein Model (HM) describes the interaction between fermions and a collection of local (dispersionless) phonon modes. In the dilute limit, the phonon degrees of freedom dress the fermions, giving rise to polaron and bipolaron formation. At higher densities, the phonons mediate collective superconducting (SC) and charge density wave (CDW) phases. Quantum Monte Carlo (QMC) simulations have considered both these limits, but have not yet focused on the physics of more general phonon spectra. Here we report QMC studies of the role of phonon dispersion on SC and CDW order in such models. We quantify the effect of finite phonon bandwidth and curvature on the critical temperature $T_{\rm cdw}$ for CDW order, and also uncover several novel features of diagonal long range order in the phase diagram, including a competition between charge patterns at momenta ${\bf q}=(\pi,\pi)$ and ${\bf q}=(0,\pi)$ which lends insight into the relationship between Fermi surface nesting and the wavevector at which charge order occurs. We also demonstrate SC order at half-filling in situations where nonzero bandwidth sufficiently suppresses $T_{\rm cdw}$.