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Geometrically frustrated quantum impurities coupled to metallic leads havebeen shown to exhibit rich behavior with a quantum phase transition separatingKondo screened and local moment phases. Frustration in the quantum impurity canalternatively be introduced via Kitaev-couplings between different spins of theimpurity cluster. We use the Numerical Renormalization Group (NRG) to study arange of systems where the quantum impurity comprising a Kitaev cluster iscoupled to a bath of non-interacting fermions. The models exhibits acompetition between Kitaev and Kondo dominated physics depending on whether theKitaev couplings are greater or less than the Kondo temperature. Wecharacterize the ground state properties of the system and determine thetemperature dependence of the crossover scale for the emergence offractionalized degrees of freedom in the model. We also demonstratequalitatively as well as quantitatively that in the Kondo limit, the compleximpurity can be mapped to an effective two-impurity system, where the emergentspin $1/2$ comprises of both Majorana and flux degrees of freedom. For atetrahedral-shaped Kitaev cluster, an extra orbital degree of freedom closelyrelated to a flux degree of freedom remains unscreened even in the presence ofboth Heisenberg and Kondo interactions.

Competition between Kondo and Kitaev Physics in Kitaev clusters coupled to a fermionic bath