  Two-dimensional (2D) ferroelectric (FE) materials are promising compounds for
next-generation nonvolatile memories, due to their low energy consumption and
high endurance. Among them, {\alpha}-In$_{2}$Se$_{3}$ has drawn particular
attention due to its in- and out-of-plane ferroelectricity, whose robustness
has been demonstrated down to the monolayer limit. This is a relatively
uncommon behavior since most bulk FE materials lose their ferroelectric
character at the 2D limit due to depolarization field. Using angle resolved
photoemission spectroscopy (ARPES), we unveil another unusual 2D phenomena
appearing in 2H \alpha-In$_{2}$Se$_{3}$ single crystals, the occurrence of a
highly metallic two-dimensional electron gas (2DEG) at the surface of
vacuum-cleaved crystals. This 2DEG exhibits two confined states which
correspond to an electron density of approximatively 10$^{13}$
electrons/cm$^{3}$, also confirmed by thermoelectric measurements. Combination
of ARPES and density functional theory (DFT) calculations reveals a direct band
gap of energy equal to 1.3 +/- 0.1 eV, with the bottom of the conduction band
localized at the center of the Brillouin zone, just below the Fermi level. Such
strong n-type doping further supports the quantum confinement of electrons and
the formation of the 2DEG.
