重新审视均匀电子气追求适当赋范从头Eliashberg理论
Revisiting the homogeneous electron gas in pursuit of the properly normed ab initio Eliashberg theory
摘要：
本文从第一性原理出发，讨论了如何在声子介导的超导体中准确地考虑屏蔽电子-电子库仑相互作用的自能效应。在Eliashberg超导体理论中，通常使用电子-空穴空间中的$2\times 2$ Pauli矩阵来分解自能。我们研究如何对角（$σ_{0}$和$σ_{3}$）组件导致准粒子校正正常状态，$Z$和$χ$条款，在均匀电子气中的行为，以建立一个规范的处理这些组件在实际的金属系统。在$G_{0}W_{0}$近似，我们指出，这些组件是非解析附近的费米面，但其方向的衍生物和由此产生的修正准粒子的速度，但定义良好。结合$G_{0}W_{0}$近似和Eliashberg方程的计算表明，有效质量和对强度以不同的方式显著地依赖于$Z$和$χ$.没有数值要求的$χ$长期的计算，因此被证明是无法描述均匀的电子气极限。这一结果对精确的第一性原理Eliashberg理论提出了挑战。
英文摘要：
We address an issue of how to accurately include the self energy effect of the screened electron-electron Coulomb interaction in the phonon-mediated superconductors from first principles. In the Eliashberg theory for superconductors, self energy is usually decomposed using the $2\times 2$ Pauli matrices in the electron-hole space. We examine how the diagonal ($σ_{0}$ and $σ_{3}$) components resulting in the quasiparticle correction to the normal state, $Z$ and $χ$ terms, behave in the homogeneous electron gas in order to establish a norm of treating those components in real metallic systems. Within the $G_{0}W_{0}$ approximation, we point out that these components are non-analytic near the Fermi surface but their directional derivatives and resulting corrections to the quasiparticle velocity are nevertheless well defined. Combined calculations using the $G_{0}W_{0}$ approximation and Eliashberg equations show us that the effective mass and pairing strength strikingly depend on both $Z$ and $χ$, in a different manner. The calculations without the numerically demanding $χ$ term is thus shown to be incapable of describing the homogeneous electron gas limit. This result poses a challenge to accurate first-principles Eliashberg theory.
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