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

The mechanism responsible for the extraordinary interface conductivity of LaAlO$_{3}$ on SrTiO$_{3}$ 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 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 appearance of 1/4 oxygen vacancies per AlO$_{2}$ sub-layer at the LaAlO$_{3}$ surface accompanied by 0.5$e^{-}$ charge-transfer into the interface is responsible for interface conductivity and the discontinuous transition in LaAlO$_{3}$/SrTiO$_{3}$. Our model also explain properties of LaAlO$_{3}$/SrTiO$_{3}$ prepared with different growth conditions.