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The mechanism responsible for the extraordinary interface conductivity of on and its insulator-metal transition remains controversial. Here, using density functional theory calculations, we establish a comprehensive and coherent picture that the interplay of electronic reconstructions, lattice distortions, and surface oxygen vacancies fully compensates the polarization potential divergence in , explaining naturally the experimental observations under different conditions. While lattice distortions and a charge redistribution between LaO and sublayers play a dominant role in the insulating state, a spontaneous appearance of 1/4 oxygen vacancies per sublayer at the surface accompanied by charge transfer into the interface is responsible for interface conductivity and the discontinuous transition in . Our model also explains properties of  …