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$$<$$\mathcal C$$<$$1/2$, differential conductance reaches some non-vanishing fraction of its unitary value. Using conformal field theory approach we analyze behavior of the quantum transport observables and residual entropy in both semiclassical regimes. We show that the semiclassical limit ii) preserves the key features of resonance scattering and the most essential fingerprints of the non-Fermi liquid behavior. We discuss possible realization of two semiclassical regimes in semiconductor quantum transport experiments.