Quantum Confinement and Electronic Structure at the Surface of van der Waals Ferroelectric {\alpha}-In$_{2}$Se$_{3}$

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.