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.
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