The electronic structure of Bi2Se3 is studied by angle-resolved photoemission and density functional theory. We show that the instability of the surface electronic properties, observed even in ultra-high-vacuum conditions, can be overcome via in-situ potassium deposition. In addition to accurately setting the carrier concentration, new Rashba-like spin-polarized states are induced, with a tunable, reversible, and highly stable spin splitting. Ab-initio slab calculations reveal that these Rashba state are derived from the 5QL quantum-well states. While the K-induced potential gradient enhances the spin splitting, this might be already present for pristine surfaces due to the symmetry breaking of the vacuum-solid interface.
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