Overscreened Kondo problem with large spin and large number of orbital channels: Two distinct semiclassical limits in quantum transport observables

We investigate the quantum transport through Kondo impurity assuming both a large number of orbital channels $\mathcal K$$\gg $$1\( for the itinerant electrons and a semi-classical spin \){\cal S}\( \)\gg \( \)1\( for the impurity. The non-Fermi liquid regime of the Kondo problem is achieved in the overscreened sector \)\mathcal K>2\mathcal{S}\(. We show that there exist two distinct semiclassical regimes for the quantum transport through impurity: i) \)\mathcal K\( \)\gg\( \)\mathcal S\( \)\gg\( \)1\(, differential conductance vanishes and ii) \)\mathcal S$$/$$\mathcal K{=}\mathcal C\( with \) 0$$