[论文解读] Quantum Phase Transition Induced by a Preformed Pair in a Boson-Fermion Model of Fulleride Superconductivity

Richard H. Squire, N. H. March|ArXiv.org|Apr 9, 2008

Fullerene Chemistry and Applications参考文献 4被引用 4

一句话总结

本文提出了一种由预形成对驱动的富勒烯超导体中的量子相变（QPT），通过费米子-玻色子框架进行建模。通过掺杂调节以实现费什巴赫共振，顶点修正破坏了米格尔定理，使超导性从BCS型转变为BEC型（共振）行为，其中预形成对稳定了单重态CDW态，抑制了BCS配对，同时实现了共振配对。

ABSTRACT

There continues to be enormous interest in the BCS to BEC transition as there still is no exact theory. We recently reported a revealing reinterpretation of the condensed phase Boson-Fermion Model (BFM) by comparing it to a cold atom formulation [1]. While the ground and singly excited states appear to remain continuous in all models we have examined, the collective modes contain a singularity due to a Feshbach resonance (tuned by doping) causing a breakdown of the Migdal theorem. As a result of vertex corrections, there is a fundamental change in the nature of the superconductivity due to the formation of preformed pairs as the previously suggested location [1] of a quantum critical point in the fulleride phase diagram is passed. The result is a quantum phase transition (QPT) between BCS and BEC-like (or Feshbach resonance) superconductivity (SC). We discuss features of the resonance and the role of the experimentally observed preformed pair formation in fullerides, essential to the Boson-Fermion Model (BFM), and often speculated since the work of Nozieres and Schmitt-Rink [17]. Here, we present arguments to establish a model of the preformed pair which can be favorably compared to a circular charge density wave (CDW) isolated on a fulleride molecule. The binding is much larger than a Cooper pair. The CDW seems to be stabalized by splitting of the Jahn-Teller active vibrational modes to reduce Coulomb repulsions. Our conclusions are: 1) the doping of two electrons into triply degenerate orbitals results in the experimentally observed singlet state (CDW); and 2) this CDW (preformed pair) has a dual role as doping is varied: suppression of BCS SC and enabling a Feshbach resonance form of SC.

研究动机与目标

• 在统一的理论框架内解释富勒烯中实验观测到的预形成对形成机制。
• 阐明富勒烯中从BCS型到BEC型超导性转变的机制。
• 确立掺杂诱导的费什巴赫共振在驱动量子相变中的作用。
• 将C60分子上单重态电荷密度波（CDW）的形成与预形成对的稳定联系起来。
• 解决强关联效应下顶点修正导致米格尔定理失效的问题。

提出的方法

• 将玻色子-费米子模型（BFM）应用于描述富勒烯中的电子配对，将预形成对视为玻色型自由度。
• 引入由掺杂调控的费什巴赫共振，改变有效相互作用并触发量子临界点。
• 对自能应用顶点修正，破坏米格尔定理，改变超导配对的性质。
• 将预形成对建模为C60分子上的局域单重态CDW，其由Jahn-Teller形变稳定，从而降低库仑排斥。
• 采用平均场方法分析BCS与BEC型超导相之间的转变。
• 将该模型与冷原子系统进行比较，以验证费什巴赫共振机制及其对集体模式的影响。

实验结果

研究问题

• RQ1 富勒烯中预形成对的形成如何导致BCS与BEC型超导性之间的量子相变？
• RQ2 掺杂在调控玻色子-费米子模型中驱动相变的费什巴赫共振中起什么作用？
• RQ3 由于顶点修正导致的米格尔定理失效如何改变超导配对机制？
• RQ4 C60上环形电荷密度波（CDW）以何种方式稳定预形成对并抑制BCS配对？
• RQ5 在三重简并轨道中掺杂两个电子后，富勒烯中观察到的单重态的起源是什么？

主要发现

• 向C60的三重简并轨道中掺杂两个电子可形成稳定的单重态CDW态，与实验观测一致。
• CDW作为预形成对，其结合能显著大于库珀对，由振动模式的Jahn-Teller分裂稳定。
• 由于费什巴赫共振引起的顶点修正破坏了米格尔定理，从根本上改变了超导配对机制。
• 在临界掺杂浓度处发生量子相变，从BCS型转变为费什巴赫共振型（BEC型）超导性。
• 预形成对具有双重作用：抑制BCS超导性，同时通过费什巴赫机制实现共振型超导性。
• 由于费什巴赫共振，集体模式表现出奇点，表明标准微扰处理的失效，证实了真正的量子临界点。