We study a multiorbital Hubbard model coupled to local Jahn-Teller phonons to investigate the superconducting state realized in fullerides. A weak-coupling approach is employed in combination with a local self-energy approximation. In addition to the normal and anomalous self-energies of the electrons, we consider the phonon self-energy, which allows a self-consistent treatment of the energetics. The frequency dependence of the self-energies and their characteristic coefficients, such as renormalization factors and dampings, are investigated in detail using numerical calculations. It is clarified that the anisotropic phonons play an important role in the stabilization of the superconducting state. By comparing the full results with those without phonon self-energies, we show that the superconductivity is stabilized by the softening of the phonon frequency. The effects of electronic fluctuations are also considered, and shown to lead to the coupling to orbitons, an analog of plasmons in the electron gas. This additional contribution further stabilizes the superconducting state.

中文翻译：

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Jahn-Teller-Hubbard 模型的 Eliashberg 理论

我们研究了与局部 Jahn-Teller 声子耦合的多轨道 Hubbard 模型，以研究在富勒里德中实现的超导状态。弱耦合方法与局部自能近似相结合。除了电子的正常和异常自能之外，我们还考虑了声子自能，它允许对能量学进行自洽处理。使用数值计算详细研究了自能的频率依赖性及其特征系数，例如重整化因子和阻尼。阐明了各向异性声子在超导态的稳定中起重要作用。通过将完整结果与没有声子自能的结果进行比较，我们表明，超导性是通过声子频率的软化来稳定的。还考虑了电子涨落的影响，并显示其导致与轨道耦合，这是电子气中等离子体的类似物。这种额外的贡献进一步稳定了超导状态。