Oxygen vacancy driven structural and orbital reconstruction on SrTiO$_{3}$ surface and subsurface

The role played by oxygen vacancies in bringing about important structural and electronic changes on oxide surfaces and interfaces have been a subject of intense scientific study. From two-dimensional electronic conductivity to the formation of magnetic states, oxygen vacancies have been suggested to be responsible for introducing a variety of interesting physical effects in bulk oxides and their surfaces. In this work, we employ Density Functional theory to perform first principles calculations of oxygen vacancy defects on SrTiO$_{3}$ surface and subsurface. In a defect free SrTiO$_{3}$ surface, the surface Ti atoms have conduction bands whose lower end comprises of split $t_{2g}$ states (lower lying degenerate $d_{xz}$ and $d_{yz}$ states and the upper lying $d_{xy}$ state). The upper conduction bands consist of split $e_{g}$ states where the $d_{z}^{2}$ orbital is shifted lower in energy with respect to the $d_{{x^2}-{y^2}}$ orbital. In the presence of an oxygen vacancy, orbitals reorder and the Ti $d_{z}^{2}$ orbitals, (which also hybridizes itself with Ti \textit{4s} state and the neighboring oxygen $p$ states) gets pushed down and occupied leading to the formation of a defect state. Formation energies of oxygen vacancies on the surface and subsurface of SrTiO$_{3}$ will be presented and the possibility of vacancy induced magnetic states on SrTiO$_{3}$ surface will be discussed.