Superconductivity of bipolarons from quadratic electron-phonon interaction

TL;DR

This paper presents a numerically exact solution for bipolarons formed via quadratic electron-phonon interaction, revealing potential for high-temperature superconductivity with specific conditions on phonon frequency and electron interactions.

Contribution

It provides the first precise numerical analysis of bipolarons from quadratic EPI, including effects of Coulomb repulsion, and estimates maximum superconducting transition temperatures.

Findings

Bipolarons form as extended soliton states at first, then shrink to atomic scale with increased coupling.

High T_c/T_Ω ratios are possible with increased phonon frequency on occupied sites.

Coulomb repulsion suppresses bipolaron formation, but stronger EPI can compensate.

Abstract

In systems with linear electron-phonon interaction (EPI), bound states of polarons, or bipolarons, form by gaining energy from the lattice deformation. The quadratic EPI case is fundamentally different: bipolarons form because electrons lose less energy when the total charge density is "compacted". As the coupling constant is increased, the bipolarons first appear as extended (but finite radius) soliton-type states. They subsequently decrease in radius until their size reaches the inter-atomic scale. We present the first numerically exact solution of the bipolaron problem from quadratic EPI in the presence of both on-site Hubbard and long-range Coulomb repulsion, and compute estimates of the largest superconducting transition temperature within the bipolaron mechanism. We find that $T_c/\Omega$ ratios, where $\Omega$ is the optical phonon frequency, can be several times larger than what one may expect from the linear EPI provided the phonon frequency is increased by orders of magnitude on occupied sites. Electron-electron repulsion can be tolerated at the expense of stronger EPI and the most detrimental effect comes from the Coulomb potential because it easily eliminates extended soliton states.