Instabilities of the Fractionalized Dirac Semimetal in the Kitaev-Kondo Model

Abstract

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 electrons 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 towards antiferromagnetic order and that superconductivity is disfavored.

Figures (5)

• Figure 1: Illustration of the Kitaev-Kondo model on a honeycomb lattice. The top layer illustrates the $S=1/2$ Kitaev QSL model with bond-directional Ising exchanges $K$. The bottom layer corresponds to tight-binding electrons with hopping amplitudes $t$ between neighboring sites of the honeycomb lattice. The local moments of the Kitaev quantum spin liquid are coupled to the conduction electrons via the conventional Kondo interaction $J_K$. A possible unit cell spanned by lattice vectors $\mathbf{a}_{1,2}=(\frac{3}{2},\pm\frac{\sqrt{3}}{2})$ is shown in green.
• Figure 2: Interaction $U$, $|J|$ and $\Gamma$ in units of $J_K^2/|K|$ and as a function of the ratio of the Fermi velocities $c$ and $v$ of Majorana fermions and Dirac conduction electrons, respectively.
• Figure 3: Second-order, one-loop diagrams that renormalize (a) the electron-electron interactions $g_i\in \{U, J, \rho \}$ and (b) the coupling vertex $\Gamma$ between conduction electrons and Majorana fermions. Conduction electron fields $\bar{\bm{\psi}}$, $\bm{\psi}$ correspond to black, Majorana fermion fields $\bm{\eta}$ to red lines.
• Figure 4: (a) RG flow of the rescaled interactions $\tilde{U}$, $\tilde{J}$, $\tilde{\rho}$, and $\tilde{\Gamma}$. The initial interaction strengths are derived from the microscopic Kitaev-Kondo model with Fermi-velocity ratio $c/v=0.2$ and for both FM (dashed) and AFM (solid) Kitaev couplings. The Kondo coupling is tuned very slightly above the critical value in both cases. (b) Same as in (a) but for $c/v=1.5$. In all cases the critical behavior is controlled by the same critical fixed point with $\tilde{\Gamma}_c=0$ and $\tilde{U}_c, \tilde{J}_c, \tilde{\rho}_c>0$, corresponding to the plateau values. (c) Fixed points and critical surface for $\tilde{\Gamma}=0$. The trajectories show the RG flow within the critical surface. The symmetry-breaking phase transition of the Kitaev-Kondo model is controlled by the critical fixed point $P_c^{(1)}$.
• Figure 5: Diagrams that contribute to the renormalization of the fields (a) $h_\textrm{CDW}$, $h_\textrm{SDW}$ and (b) $h_\textrm{SC}$ to linear order.