Charge correlations suppress unconventional pairing in the Holstein model

TL;DR

This study uses quantum Monte Carlo simulations to challenge previous claims of unconventional superconductivity in the Holstein model, showing charge correlations suppress such pairing and highlighting issues with certain theoretical approaches.

Contribution

It provides non-perturbative numerical evidence that charge correlations inhibit unconventional pairing in the Holstein model, contrasting prior theoretical predictions.

Findings

Unconventional pairing correlations do not exceed noninteracting values.

Charge-density-wave correlations dominate at low temperatures.

Vertex-corrected Migdal-Eliashberg schemes can give uncontrolled results with Fermi surface nesting.

Abstract

In a recent work by Schrodi $\textit{et al}$. [Phys. Rev. B. $\textbf{104}$, L140506 (2021)], the authors find an unconventional superconducting state with a sign-changing order parameter using the Migdal-Eliashberg theory, including the first vertex correction. This unconventional solution arises despite using an isotropic bare electron-phonon coupling in the Hamiltonian. We examine this claim using hybrid quantum Monte Carlo for a single-band Holstein model with a cuprate-like noninteracting band structure and identical parameters to Schrodi $\textit{et al}$.. Our Monte Carlo results for these parameters suggest that unconventional pairing correlations do not exceed their noninteracting values at any carrier concentration we have checked. Instead, strong charge-density-wave correlations persist at the lowest accessible temperatures for dilute and nearly half-filled bands. Lastly, we present arguments for how vertex-corrected Migdal-Eliashberg calculation schemes can lead to uncontrolled results in the presence of Fermi surface nesting.