We study the interplay between the Kondo effect and (color) superconductivity in doped Dirac metals with magnetic impurities and in quark matter with colorful impurities. We first point out that the overscreened Kondo effect arises in the normal state of these systems. Next the (color) superconducting gap is incorporated as a mean field and the phase diagram for a varying gap and temperature is constructed nonperturbatively. A rich phase structure emerges from a competition of effects unique to a multichannel system. The Kondo-screened phase is shown to disappear for a sufficiently large gap. Peculiarity of quark matter due to the confining property of non-Abelian gauge fields is noted. We also investigate the spectrum of sub-gap excited states, called Shiba states. Based on a model calculation and physical reasoning we predict that, as the coupling of the impurity to the bulk is increased, there will be more than one quantum phase transition due to level crossing among overscreened states.
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