Doped Kagome System as Exotic Superconductor

A Chern--Simons theory for the doped spin-1/2 kagom\'e system is constructed, from which it is shown that the system is an exotic superconductor that breaks time-reversal symmetry. It is also shown that the system carries minimal vortices of flux $hc/4e$ (as opposed to the usual $hc/2e$ in conventional superconductors) and contains fractional quasiparticles (including fermionic quasiparticles with \emph{semionic} mutual statistics and spin-1/2 quasiparticles with \emph{bosonic} self-statistics) in addition to the usual spin-1/2 fermionic Bougoliubov quasiparticle. Two Chern--Simons theories--one with an auxiliary gauge field kept and one with the auxiliary field and a redundant matter field directly eliminated--are presented and shown to be consistent with each other.