Role of Competing Interactions on the Nature of Carriers at a Model Polar Oxide Interface

Transport measurements of the polar oxide interfaces like LaAlO$_3$/SrTiO$_3$ have revealed a rich variety of physical properties such as a Kondo resistance minimum, metallicity, insulation, superconductivity, and possibly also magnetism under varying experimental conditions. We present a mean-field study of a model Hamiltonian, appropriate for the polar oxide interfaces, that includes the electron hopping, Jahn-Teller coupling, and Coulomb interaction terms. Our results predict the existence of a number of interesting phases, {\it viz.}, a 2D metallic or polaronic phase as well as 3D metallic or a polaronic phase depending on the relative strengths of these interactions. Under appropriate conditions, a mixed phase may also result consisting of 2D polarons and a 3D metal. In the polaronic phase, the combination of Jahn-Teller coupling and Coulomb terms could form magnetic centers. In addition, our results also reveal the possibility of a phase separation, where for some carrier concentrations, the system phase separates into a 2D like region and a 3D region. This will have important implication for the interpretation of the transport measurements. Work supported by the US Department of Energy.