  Quantum spin liquids (QSLs), in which spins are highly entangled, have been
considered a groundwork for generating exotic superconductivity.Despite
numerous efforts, superconductivity emerging from QSLs has been unrealized in
actual materials due to the difficulties in stabilizing QSL states with
metallic conductivity.Recently, an organic compound,
$\kappa$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$, with a nearly regular triangular
lattice of molecular dimers was recognized as a candidate for doped QSLs. In
this study, we report an unusual superconducting phase of
$\kappa$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$: unexpectedly large ratios of the
upper critical field to the critical temperature $H_{\rm c2}$/$T_{\rm c}$ in
fields not only parallel but also perpendicular to the two-dimensional
conducting layers and a very wide region of fluctuating superconductivity above
$T_{\rm c}$.Our results reveal that these peculiarities arise from strong
electron correlations and possible quantum criticality unique to the doped QSL
state, leading to a heavy mass of itinerant carriers and a large
superconducting energy gap.
