Stability conditions for a large anharmonic bipolaron

TL;DR

This paper explores how anharmonic 1-electron-2-phonon interactions influence the formation and stability of large bipolarons, revealing conditions that could make their experimental observation more feasible.

Contribution

It introduces a generalized Hamiltonian including anharmonic interactions and derives a semi-analytical phase diagram for bipolaron stability across all coupling strengths.

Findings

Large bipolaron formation is favored with significant 1-electron-2-phonon interaction.

The critical electron-phonon coupling strength decreases with increased anharmonic interaction.

Materials like strontium titanate are promising candidates for large bipolaron realization.

Abstract

A large polaron is a quasiparticle that consists of a nearly free electron interacting with the phonons of a material, whose lattice parameters are much smaller than the polaron scale. The electron-phonon interaction also leads to an attractive interaction between electrons, which can allow two polarons to pair up and form a bipolaron. It has been shown that large bipolarons can form in theory due to strong 1-electron-1-phonon coupling, but they have not been seen in real materials because the critical value of the required electron-phonon interaction is too large. Here, we investigate the effect of 1-electron-2-phonon coupling on the large bipolaron problem. Starting from a generalization of the Fr\"ohlich Hamiltonian that includes both the standard 1-electron-1-phonon interaction as well as an anharmonic 1-electron-2-phonon interaction, we use the path integral method to find a semi-analytical upper bound for the bipolaron energy that is valid at all values of the Fr\"ohlich coupling strength $\alpha$. We find the bipolaron phase diagram and conditions for the bipolaron stability by comparing the bipolaron energy to the energy of two free polarons. The critical value of the Fr\"ohlich coupling strength $\alpha_{\text{crit}}$ is calculated as a function of the strength of the 1-electron-2-phonon interaction. The results suggest that large bipolaron formation is more likely in materials with significant 1-electron-2-phonon interaction as well as strong 1-electron-1-phonon interaction, such as strontium titanate.