论文标题
语音在埃利亚斯贝格理论中重量化的影响2D和3D系统中超导性的影响
Influence of phonon renormalization in Eliashberg theory for superconductivity in 2D and 3D systems
论文作者
论文摘要
Eliashberg的超导性基础理论是基于Migdal近似的应用，该理论指出，如果声子和电子能量尺度之间的比率很小，则顶点校正与一阶电子量音散射相对于一阶电子散射是可以忽略的。所得理论结合了电子和声子自我富集的第一张Feynman图。但是，后者在数值分析中最常见。在这里，我们在两个维度和三个维度上提供了全面宽度Eliashberg理论的广泛研究，其中包括电子在声子频谱上的全面反应。我们揭示了嵌套特性，状态的费米表面密度，重新归一化的电子偶联，声子软化和超导性之间的复杂相互作用。我们进一步提出了针对最大可能的临界温度的扩展定律$ t_c^{\ textrm {max}} \ propto / propto / propto（ω）\ sqrt {ω_0^2-2-ω^2} $ 2D和3D系统，这两个均恢复了电子$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $。另外，我们分析了可以实现最大$ t_c $增强的电子结构属性。
Eliashberg's foundational theory of superconductivity is based on the application of Migdal's approximation, which states that vertex corrections to first order electron-phonon scattering are negligible if the ratio between phonon and electron energy scales is small. The resulting theory incorporates the first Feynman diagrams for electron and phonon self-energies. However, the latter is most commonly neglected in numerical analyses. Here we provide an extensive study of full-bandwidth Eliashberg theory in two and three dimensions, where we include the full back reaction of electrons onto the phonon spectrum. We unravel the complex interplay between nesting properties, Fermi surface density of states, renormalized electron-phonon coupling, phonon softening, and superconductivity. We propose furthermore a scaling law for the maximally possible critical temperature $T_c^{\textrm{max}}\proptoλ(Ω) \sqrt{Ω_0^2-Ω^2}$ in 2D and 3D systems, which embodies both the renormalized electron-phonon coupling strength $λ(Ω)$ and softened phonon spectrum $Ω$. Also, we analyze for which electronic structure properties a maximal $T_c$ enhancement can be achieved.
