Doping the Kane-Mele-Hubbard model: A Slave-Boson Approach

We study the Kane-Mele-Hubbard model both at half-filling and away from half-filling using a slave-boson mean-field approach at zero temperature. We obtain a phase diagram at half-filling and discuss its connection to recent results from quantum Monte Carlo, cellular dynamical mean field, slave-rotor, and $Z_2$ mean-field studies. In particular, we find a small window in parameter space where a spin liquid phase with gapped spin and charge excitations reside. Upon doping, we show the spin liquid state becomes a superconducting state by explicitly calculating the singlet pairing order parameters. Interestingly, we find an ``optimal" doping for such superconductivity. Our work reveals some of the phenomenology associated with doping an interacting system with strong spin-orbit coupling and intermediate strength electron-electron interactions.