In the classic transistor, the number of electric charge carriers—and thus the electrical conductivity—is precisely controlled by external voltage, providing electrical switching capability. This simple but powerful feature is essential for information processing technology, and also provides a platform for fundamental physics research1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16. As the number of charges essentially determines the electronic phase of a condensed-matter system, transistor operation enables reversible and isothermal changes in the system’s state, as successfully demonstrated in electric-field-induced ferromagnetism2, 3, 4 and superconductivity5, 6, 7, 8, 9, 10. However, this effect of the electric field is limited to a channel thickness of nanometres or less, owing to the presence of Thomas–Fermi screening. Here we show that this conventional picture does not apply to a class of materials characterized by inherent collective interactions between electrons and the crystal lattice. We prepared metal–insulator–semiconductor field-effect transistors based on vanadium dioxide—a strongly correlated material with a thermally driven, first-order metal–insulator transition well above room temperature17, 18, 19, 20, 21, 22, 23—and found that electrostatic charging at a surface drives all the previously localized charge carriers in the bulk material into motion, leading to the emergence of a three-dimensional metallic ground state. This non-local switching of the electronic state is achieved by applying a voltage of only about one volt. In a voltage-sweep measurement, the first-order nature of the metal–insulator transition provides a non-volatile memory effect, which is operable at room temperature. Our results demonstrate a conceptually new field-effect device, extending the concept of electric-field control to macroscopic phase control.