Polaron with Quadratic Electron-phonon Interaction

TL;DR

This paper provides a numerically exact analysis of polarons with quadratic electron-phonon coupling, revealing unique properties that differ significantly from linear polarons across various regimes and coupling strengths.

Contribution

It introduces the first exact numerical methods to study quadratic polarons and explores their properties across different regimes, filling a gap in polaron research.

Findings

Quadratic polarons are insensitive to large quadratic coupling except near instability.

Their properties depend mainly on the adiabatic ratio, not on electron dispersion or space dimension.

They exhibit weak lattice deformations even at the instability point.

Abstract

We present the first numerically exact study of a polaron with quadratic coupling to the oscillator displacement, using two alternative methodological developments. Our results cover both anti-adiabatic and adiabatic regimes and the entire range of electron-phonon coupling $g_2$, from the system's stability threshold at attractive $g_2=-1$ to arbitrary strong repulsion at $g_2 \gg 1$. Key properties of quadratic polarons prove dramatically different from their linear counterparts. They (i) are insensitive even to large quadratic coupling except in the anti-adiabatic limit near the threshold of instability at attraction; (ii) depend only on the adiabatic ratio but are insensitive to the electron dispersion and dimension of space; (iii) feature weak lattice deformations even at the instability point. Our results are of direct relevance to properties of electrons at low densities in polar materials, including recent proposals for their superconducting states.