The electronic structures and properties of heterointerfaces in the perovskite oxide superlattices ${\mathrm{LaAlO}}_{3}∕{\mathrm{SrTiO}}_{3}\phantom{\rule{0.3em}{0ex}}[001]$ are presented using the first-principles all-electron full-potential linearized augmented plane-wave (FLAPW) method. Superlattices with three types of interfaces, (i) electron-doped, (ii) hole-doped, and (iii) both electron- and hole-doped, are studied and compared. For the electron-doped interface, the mixed valency of Ti along with the Jahn-Teller effect are found to explain the metallicity, in agreement with experiment, whereas for the hole-doped interface metallicity is found, in contrast to experiment. Oxygen vacancies introduce an additional $n$-type carrier to compensate the holes present at the interface, which now becomes insulating and agrees well with experiment. For a system with both types of interfaces, the metallicity found for the unrelaxed structure is changed to insulating after relaxation is included. For all cases, the relaxation results in a complicated buckled geometry, which is a good indication of the adjustment due to polarity discontinuity. Our findings support recent experimental results, namely, (i) the mixed-valence character of Ti at the electron-doped interface, and (ii) the existence and importance of oxygen vacancies at the hole-doped interface.
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