Superconductivity of bipolarons from quadratic electron-phonon interaction

Zhongjin Zhang, Anatoly Kuklov, Nikolay Prokof'ev, Boris Svistunov
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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.
二次电子-声子相互作用产生的双极子超导性
在具有线性电子-声子相互作用(EPI)的系统中,极子的束缚态或双极子通过从晶格变形中获得能量而形成。随着耦合常数的增加,双极子首先以扩展(但半径无限)的孤子型状态出现。随后,它们的半径逐渐减小,直至达到原子间尺度。我们首次提出了在存在现场哈伯德斥力和长程库仑斥力的情况下,由二次 EPI 得到的双极子问题的精确数值解,并计算了双极子机制中最大超导转变温度的估计值。我们发现,如果声子频率在所占位点上增加了几个数量级,那么$T_c/\Omega$比(其中$\Omega$是光声子频率)可能会比人们从线性 EPI 中预期的大几倍。电子-电子斥力可以容忍,但要以更强的 EPI 为代价,最有害的影响来自库仑势,因为它很容易消除延伸的孤子态。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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