The effects of non-linear electron-phonon interactions on superconductivity and charge-density-wave correlations

TL;DR

This study uses quantum Monte Carlo simulations to show that non-linear electron-phonon interactions significantly suppress charge-density-wave correlations and negatively impact superconductivity, highlighting their importance in finite carrier systems.

Contribution

It provides the first detailed analysis of how non-linear electron-phonon interactions affect superconductivity and charge-density waves in a 2D Holstein-like model.

Findings

Non-linear interactions dramatically suppress CDW correlations.

Non-linearity is detrimental to superconductivity at finite temperatures.

Phonon hardening and coupling renormalization explain these effects.

Abstract

Determinant quantum Monte Carlo (DQMC) simulations are used to study non-linear electron-phonon interactions in a two-dimensional Holstein-like model on a square lattice. We examine the impact of non-linear electron-lattice interactions on superconductivity and on Peierls charge-density-wave (CDW) correlations at finite temperatures and carrier concentrations. We find that the CDW correlations are dramatically suppressed with the inclusion of even a small non-linear interaction. Conversely, the effect of the non-linearity on superconductivity is found to be less dramatic at high temperatures; however, we find evidence that the non-linearity is ultimately detrimental to superconductivity. These effects are attributed to the combined hardening of the phonon frequency and a renormalization of the effective linear electron-phonon coupling towards weaker values. These results demonstrate the importance of non-linear interactions at finite carrier concentrations when one is addressing CDW and superconducting order and have implications for experiments that drive the lattice far from equilibrium.