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

Abstract

We investigate quantum transport through the Kondo impurity assuming both a large number of orbital channels $\mathcal{K}\ensuremath{\gg}1$ for the itinerant electrons and a semiclassical spin $\mathcal{S}\phantom{\rule{4pt}{0ex}}\ensuremath{\gg}\phantom{\rule{4pt}{0ex}}1$ 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) $\mathcal{K}\phantom{\rule{4pt}{0ex}}\ensuremath{\gg}\phantom{\rule{4pt}{0ex}}\mathcal{S}\phantom{\rule{4pt}{0ex}}\ensuremath{\gg}\phantom{\rule{4pt}{0ex}}1$, differential conductance vanishes, and (ii) $\mathcal{S}/\mathcal{K}=\mathcal{C}$ with $0<\mathcal{C}<1/2$, differential conductance reaches some nonvanishing fraction of its unitary value. Using the conformal field theory approach we analyze the 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.