Higher-order Fermi-liquid corrections for an Anderson impurity away from half-filling

Abstract

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-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 {\bf 95}, 165404 (2017)]. In our formulation, the Fermi-liquid parameters such as the quasi-particle energy, damping, and transport coefficients are related to each other through the total vertex ${\Gamma }_{\sigma {\sigma }^{\prime };{\sigma }^{\prime }\sigma }(\omega ,{\omega }^{\prime };{\omega }^{\prime },\omega )$, which may be regarded as a generalized Landau quasi-particle interaction. We obtain exactly this function up to linear order with respect to the frequencies $\omega$ and ${\omega }^{\prime }$ using the anti-symmetry and analytic properties. The coefficients acquire additional contributions of three-body fluctuations away from half-filling through the non-linear susceptibilities. We also apply the formulation to non-equilibrium transport through a quantum dot, and clarify how the zero-bias peak evolves in a magnetic field.

5 pages, 2 figures, Introduction has been revised

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