A comparative study of the superconductivity in the Holstein and optical Su-Schrieffer-Heeger models

TL;DR

This study compares superconductivity mechanisms in Holstein and SSH models, revealing SSH supports lighter bipolarons and stronger superconductivity at higher couplings, with implications for designing bipolaronic superconductors.

Contribution

It provides a detailed numerical comparison of pairing and charge correlations in Holstein and SSH models, highlighting the conditions favoring bipolaronic superconductivity.

Findings

SSH supports light bipolarons and strong pairing at large e-ph coupling.

Holstein favors heavy bipolarons and charge-density-wave order.

Weak coupling pairing correlations are similar in both models.

Abstract

Theoretical studies suggest that Su-Schrieffer-Heeger-like electron-phonon ($e$-ph) interactions can mediate high-temperature bipolaronic superconductivity that is robust against repulsive electron-electron interactions. Here we present a comparative analysis of the pairing and competing charge/bond correlations in the two-dimensional Holstein and optical Su-Schrieffer-Heeger (SSH) models using numerically exact determinant quantum Monte Carlo. We find that the SSH interactions support light bipolarons and strong superconducting correlations out to relatively large values of the $e$-ph coupling $\lambda$ and densities near half-filling, while the Holstein interaction does not due to the formation of heavy bipolarons and competing charge-density-wave order. We further find that the Holstein and SSH models have comparable pairing correlations in the weak coupling limit for carrier concentrations $\langle n \rangle \ll 1$, where competing orders and polaronic effects are absent. These results support the proposal that SSH (bi)polarons can support superconductivity to larger values of $\lambda$ in comparison to the Holstein polaron, but that the resulting $T_\mathrm{c}$ gains are small in the weak coupling limit. We also find that the SSH model's pairing correlations are suppressed after including a weak on-site Hubbard repulsion. These results have important implications for identifying and engineering bipolaronic superconductivity.