Analytical Perturbative Treatment of Multiterminal Nonequilibrium Anderson Impurity Models

We investigate analytically the nonequilibrium Anderson impurity model connecting with multiterminal leads\footnote{N.~Taniguchi, Phys. Rev. B \textbf{90} 115421 (2014).}. Within the validity of the second-order perturbation regarding the interaction strength, the full dependence on frequency and bias voltage of the nonequilibrium self-energy and spectral function is determined for a generic multiterminal setting where the current preservation has been an issue.\footnote{S.~Hershfield \textit{et al.}, Phys. Rev. B \textbf{46}, 7046 (1992).} Our analytical perturbative treatment respects the current conservation as well as the spectral sum rule, and it encompasses Fermi-liquid and non-Fermi liquid behaviors, showing that increasing finite-bias voltage leads to a crossover from the Kondo resonance to the Coulomb blockade phenomena. Analysis on two-terminal and multiterminal settings shows that finite-bias voltage does not split the Kondo resonance in this order; no specific structure due to multiple leads emerges in the spectral function. Overall bias dependence is quite similar to finite-temperature effect, which could be understood by help of the Ward identity and the limit of $N\gg 1$ terminals.