  A quantum spin liquid (QSL) would be an exotic stage for superconductivity. A
promising candidate for a doped QSL is the organic triangular-lattice system,
kappa-(BEDT-TTF)4Hg2:89Br8, which hosts a non-Fermi liquid and magnetism of a
QSL nature and shows superconductivity upon cooling. Here, we report that its
superfluid density is anomalously reduced, indicating the existence of
substantial incoherent spectral weight and weak superconducting phase
stiffness. Moreover, the ratio of the superconducting transition temperature to
the nominal Fermi temperature is as large as 0.1, orders of magnitude beyond
typical BCS values. These observations in a system free from competing orders
that complicate the similar issue in underdoped cuprates give a clue to the
enigmatic missing superfluid density in doped Mott insulators.
