Structural Basis of Conduction at LaAlO$_{3}$-SrTiO$_{3}$ Interfaces*

We present new results on the application of the x-ray phase retrieval method, Coherent Bragg Rod Analysis (COBRA), to heteroepitaxial interfaces in LaAlO$_{3}$ thin films grown on SrTiO$_{3}$ substrates, a system known to form an interfacial quasi-2D electron gas. We observe a dilated, mixed-valence interface which modifies the electronic band structure, lowering the minimum of the conduction band below the Fermi level and thereby rendering the dilated interface conducting. In particular the COBRA measurements reveal the formation of an interfacial La,SrTiO$_{3}$ layer with an accumulation of trivalent Ti at the interface which is responsible for the lattice dilation and minimizes the electrostatic energy at the TiO$_{2}$-terminated SrTiO$_{3}$ substrate surface. The work presented here establishes a structural basis for the formation of the conducting interface.