Chiral superconductivity with full Bogoliubov Fermi surface in a doped Kagome spin-liquid state.*

We employ a large-scale variational Monte-Carlo simulation to investigate the lightly doped t-J model on the Kagome lattice. We propose several new variational states which smoothly connect to the previously studied uniform 0-flux or U(1) $\pi$-flux states. By comparing the energies of a variety of trail-states at several system-sizes, we find that the state with lowest energy is a chiral superconducting state with full Bogoliubov Fermi surface, which can be analogous to the Fulde-Ferrell-Larkin-Ovchinnikov state. The physical properties of this new state and the experimental consequences of the existence of Bogoliubov Fermi surface in this superconducting state are discussed.