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We study the interplay between the Kondo effect and (color) superconductivityin doped Dirac metals with magnetic impurities and in quark matter withcolorful impurities. We first point out that the overscreened Kondo effectarises in the normal state of these systems. Next the (color) superconductinggap is incorporated as a mean field and the phase diagram for a varying gap andtemperature is constructed nonperturbatively. A rich phase structure emergesfrom a competition of effects unique to a multichannel system. TheKondo-screened phase is shown to disappear for a sufficiently large gap.Peculiarity of quark matter due to the confining property of non-Abelian gaugefields is noted. We also investigate the spectrum of sub-gap excited states,called Shiba states. Based on a model calculation and physical reasoning wepredict that, as the coupling of the impurity to the bulk is increased, therewill be more than one quantum phase transition due to level crossing amongoverscreened states.

Overscreened Kondo effect, (color) superconductivity and Shiba states in Dirac metals and quark matter