Localized electron states and phase separation at the LaAlO$_3$/SrTiO$_3$ interface

Even though the 2D electron gas at the polar interfaces of LAO/STO has been studied extensively, an explanation for the observed magnetic centers or the coexistence of magnetism and superconductivity is still lacking. Earlier density-functional calculations have indicated the presence of multi-bands and two types of electrons at the interface [1]. Here we propose that a combination of lattice disorder, octahedral rotations, and Jahn-Teller distortion can lead to some of these electrons to be localized near the interface and form lattice polarons. Evidence for this is presented from detailed density-functional calculations, which indicate that the energy gain associated with JT distortion and impurity or disorder induced local potentials can offset the kinetic energy cost of localization. Our model studies [2] also show the possible existence of a phase separation, thereby providing a natural explanation for the coexistence of magnetism and superconductivity [3].\\[4pt] [1] Z. S. Popovi\'{c}, S. Satpathy and R. M. Martin {\it Phys. Rev. Lett.}, {\bf 101}, 256801 (2008)\\[0pt] [2] B. R. K. Nanda and S. Satpathy {\it Phys. Rev B}, {\bf 83}, 195114 (2011)\\[0pt] [3] L. Li {\it et. al.} {\it Nature Physics}, {\bf 7}, 762 (2011); J. A. Bert {\it et. al.} {\it ibid}, 767 (2011);