We report a Rashba spin splitting of a two-dimensional electron gas in the topological insulator Bi$_2$Se$_3$ from angle-resolved photoemission spectroscopy. We further demonstrate its electrostatic control, and show that spin splittings can be achieved which are at least an order-of-magnitude larger than in other semiconductors. Together these results show promise for the miniaturization of spintronic devices to the nanoscale and their operation at room temperature.
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