Order Fractionalization in a Kitaev-Kondo model

We describe a mechanism for order fractionalization in a two-dimensional Kondo lattice model, in which electrons interact with a gapless spin liquid of Majorana fermions described by the Yao-Lee (YL) model. When the Kondo coupling to the conduction electrons exceeds a critical value, the model develops a superconducting instability into a state where the spinor order parameter carries charge $e$ and spin $S=1/2$. The broken symmetry state develops a gapless Majorana Dirac cone in the bulk. By including an appropriate gauge string, we can show that the charge $e$, spinorial order develops off-diagonal long range order that allows electrons to coherently tunnel arbitrarily long distances through the spin liquid.