  In this paper, we study the lightly doped Kitaev spin liquid (DKSL) and find
it to be a Fermi liquid state. The DKSL has a closed Fermi surface around the
center of the Brillouin zone with the quantized volume determined by the
Luttinger's theorem. It has well-defined quasiparticles near the Fermi surface
and can be detected in the angle-resolved photoemission spectroscopy. The DKSL
has the topological Kitaev spin liquid (KSL) as its neutral background. It
violates the Wiedemann-Franz law and has a large Wilson ration. These results
has the potential experimental test in the iridates upon doping.
