  The Mott metal-insulator transition-a drastic manifestations of Coulomb
interactions among electrons-is the first-order transition of clear
discontinuity, as shown by various experiments and the celebrated dynamical
mean-field theory. Recent theoretical works, however, suggest that the
transition is continuous if the Mott insulator carries an exotic spin liquid
with a spinon Fermi surface. Here, we demonstrate the case of a
quasi-continuous Mott transition from a Fermi liquid to a spin liquid in an
organic triangular-lattice system k-(ET)2Cu2(CN)3. Transport experiments
performed under fine pressure tuning find that, as the Mott transition is
approached, the Fermi-liquid coherence temperature continuously falls to the
scale of kelvins with divergent quasi-particle decay rate in the metal side and
the charge gap gradually closes in the insulator side. The Clausius-Clapeyron
analysis of the pressure-temperature phase diagram provides thermodynamic
evidence for the extremely weak first-order nature of the Mott transition.
These results suggest that the spin liquid hosts a spinon Fermi surface, which
turns into an electron Fermi surface when charges are Mott delocalized.
