Instabilities of the fractionalized Dirac semimetal in the Kitaev-Kondo model

We study a honeycomb Kondo lattice model in which Dirac conduction electrons are coupled to a spin-1/2 Kitaev quantum spin liquid. For weak Kondo coupling, the spins fractionalize into Majorana fermions comprising a gapless Dirac mode and three gapped visons. In second order perturbation theory, the Kondo coupling gives rise to local Hubbard repulsions and spin-spin interactions between conduction electrons, as well as a vertex coupling electron to gapless Majorana fermions. We analyze the resulting low-energy field theory using a perturbative renormalization group (RG) scheme, accounting for additional density-density interactions generated under RG. At criticality, electrons decouple from Majorana fermions but all three electron interactions acquire positive values. An analysis of susceptibility exponents reveals that the fractionalized Fermi liquid becomes unstable toward antiferromagnetic order and that superconductivity is disfavored.