We study the higher-order Fermi-liquid relations of Kondo systems for arbitrary impurity-electron fillings, extending the many-body quantum theoretical approach of Yamada and Yosida. It includes, partly, a microscopic clarification of the related achievements based on Nozières’ phenomenological description: Filippone, Moca, von Delft, and Mora [Phys. Rev. B 95, 165404 (2017)]. In our formulation, the Fermi-liquid parameters such as the quasiparticle energy, damping, and transport coefficients are related to each other through the total vertex ${\mathrm{\Gamma }}_{\sigma {\sigma }^{\prime };{\sigma }^{\prime }\sigma }(\omega ,{\omega }^{\prime };{\omega }^{\prime },\omega )$, which may be regarded as a generalized Landau quasiparticle interaction. We obtain exactly this function up to linear order with respect to the frequencies $\omega$ and ${\omega }^{\prime }$ using the antisymmetry and analytic properties. The coefficients acquire additional contributions of three-body fluctuations away from half filling through the nonlinear susceptibilities. We also apply the formulation to nonequilibrium transport through a quantum dot, and clarify how the zero-bias peak evolves in a magnetic field.

中文翻译：

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远离半填充的安德森杂质的高阶费米液体校正

我们研究了任意杂质电子填充物的近藤系统的高阶费米液体关系，扩展了山田和吉田的多体量子理论方法。它部分包括基于诺齐耶尔现象学描述的相关成就的微观澄清：菲利彭，莫卡，冯·代尔夫特和莫拉[ Phys。版本B 95，165404（2017）]。在我们的公式中，费米液体参数（如准粒子能量，阻尼和传输系数）在整个顶点之间相互关联${\mathrm{\Gamma }}_{\sigma {\sigma }^{\prime };{\sigma }^{\prime }\sigma }（\omega ，{\omega }^{\prime };{\omega }^{\prime }，\omega ）$，这可以看作是广义的Landau拟粒子相互作用。我们精确地获得了关于频率的线性函数$\omega$ 和 ${\omega }^{\prime }$使用反对称和解析属性。系数通过非线性磁化率获得了三体涨落的贡献，而这与半填充不一样。我们还将该公式应用于通过量子点的非平衡传输，并阐明了零偏峰在磁场中如何演化。