  Geometrically frustrated quantum impurities coupled to metallic leads have
been shown to exhibit rich behavior with a quantum phase transition separating
Kondo screened and local moment phases. Frustration in the quantum impurity can
alternatively be introduced via Kitaev-couplings between different spins of the
impurity cluster. We use the Numerical Renormalization Group (NRG) to study a
range of systems where the quantum impurity comprising a Kitaev cluster is
coupled to a bath of non-interacting fermions. The models exhibits a
competition between Kitaev and Kondo dominated physics depending on whether the
Kitaev couplings are greater or less than the Kondo temperature. We
characterize the ground state properties of the system and determine the
temperature dependence of the crossover scale for the emergence of
fractionalized degrees of freedom in the model. We also demonstrate
qualitatively as well as quantitatively that in the Kondo limit, the complex
impurity can be mapped to an effective two-impurity system, where the emergent
spin $1/2$ comprises of both Majorana and flux degrees of freedom. For a
tetrahedral-shaped Kitaev cluster, an extra orbital degree of freedom closely
related to a flux degree of freedom remains unscreened even in the presence of
both Heisenberg and Kondo interactions.
