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The mechanism responsible for the extraordinary interface conductivity ofLaAlO$_{3}$ on SrTiO$_{3}$ and its insulator-metal transition remainscontroversial. Here, using density functional theory calculations, we establisha comprehensive and coherent picture that the interplay of electronicreconstructions, lattice distortions, and surface oxygen vacancies fullycompensates the polarization potential divergence in LaAlO$_{3}$/SrTiO$_{3}$,explaining naturally the experimental observations under different conditions.While lattice distortions and a charge redistribution between LaO and AlO$_2$sub-layers play a dominant role in insulating state, a spontaneous appearanceof 1/4 oxygen vacancies per AlO$_{2}$ sub-layer at the LaAlO$_{3}$ surfaceaccompanied by 0.5$e^{-}$ charge-transfer into the interface is responsible forinterface conductivity and the discontinuous transition inLaAlO$_{3}$/SrTiO$_{3}$. Our model also explain properties ofLaAlO$_{3}$/SrTiO$_{3}$ prepared with different growth conditions.

The interplay of electronic reconstructions, lattice distortions, and  surface oxygen vacancies in insulator-metal transition of  LaAlO$_{3}$/SrTiO$_{3}$