17 pages, 6 figures, published in PRBInternational audienceUsing a Fermi liquid approach, we provide a comprehensive treatment of the current and current noise through a quantum dot whose low-energy behaviour corresponds to an SU($N$) Kondo model, focusing on the case N=4 relevant to carbon nanotube dots. We show that for general $N$, one needs to consider the effects of higher-order Fermi liquid corrections even to describe low-voltage current and noise. We also show that the noise exhibits complex behaviour due to the interplay between coherent shot noise, and noise arising from interaction-induced scattering events. We treat various imperfections relevant to experiments, such as the effects of asymmetric dot-lead couplings
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