Unconventional superconductivity typically occurs in materials in which a small change of a parameter such as bandwidth or doping leads to antiferromagnetic or Mott insulating phases. As such competing phases are approached, the properties of the superconductor often become increasingly exotic. For example, in organic superconductors and underdoped high-$T_mathrm{c}$ cuprate superconductors a fluctuating superconducting state persists to temperatures significantly above $T_mathrm{c}$. By studying alloys of quasi-two-dimensional organic molecular metals in the $kappa$-(BEDT-TTF)$_2$X family, we reveal how the Nernst effect, a sensitive probe of superconducting phase fluctuations, evolves in the regime of extreme Mott criticality. We find strong evidence that, as the phase diagram is traversed through superconductivity towards the Mott state, the temperature scale for superconducting fluctuations increases dramatically, eventually approaching the temperature at which quasiparticles become identifiable at all.
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