Raslan, Amany Khalil

Experiments have observed a two-dimensional electron gas at the interface of two insulating oxides: strontium titanate (SrTiO₃) and lanthanum aluminate (LaAlO₃). These interfaces exhibit metallic, superconducting, and magnetic behaviours, which are strongly affected by impurities. Motivated by experiments, we introduce a simple model in which impurities lie at the interface. We treat the LaAlO₃ as an insulator and model the SrTiO₃ film. By solving a set of self-consistent Hartree equations for the charge density, we obtain the band structure of the SrTiO₃ film. We then study the relative contributions made by the occupied bands to the two-dimensional conductivity of the LaAlO₃/SrTiO₃ interface. We find that the fractional conductivity of each band depends on several parameters: the mass anisotropy, the filling, and the impurity potential.

Author Keywords: conductivity, impurities, insulating oxides, Two-dimensional electron gases

We build a theoretical model for exploring the electronic properties of the two-dimensional (2D) electron gas that forms at the interface between insulating SrTiO3 (STO) and a number of perovskite materials including LaTiO3, LaAlO3, and GdTiO3. The model treats conduction electrons within a tight-binding approximation, and the dielectric polarization via a Landau-Devonshire free energy that incorporates STO's strongly nonlinear, nonlocal, field-, and temperature-dependent dielectric response. We consider three models for the dielectric polarization at the interface: an ideal-interface model in which the interface has the same permittivity as the bulk, a dielectric dead-layer model in which the interface has permittivity lower that the bulk, and an interfacial-strain model in which the strain effects are included.

The ideal-interface model band structure comprises a mix of quantum 2D states that are tightly bound to the interface, and quasi-three-dimensional (3D) states that extend hundreds of unit cells into the STO substrate. We find that there is a substantial shift of electrons away from the interface into the 3D tails as temperature is lowered from 300 K to 10 K. We speculate that the quasi-3D tails form the low- density high-mobility component of the interfacial electron gas that is widely inferred from magnetoresistance measurements.

Multiple experiments have observed a sharp Lifshitz transition in the band structure of STO interfaces as a function of applied gate voltage. To understand this transition, we first propose a dielectric dead-layer model. It successfully predicts the Lifshitz transition at a critical charge density close to the measured one, but does not give a complete description for the transition. Second, we use an interfacial-strain model in which we consider the electrostrictive and flexoelectric coupling between the strain and polarization. This coupling generates a thin polarized layer whose direction reverses at a critical density. The transition occurs concomitantly with the polarization reversal. In addition, we find that the model captures the two main features of the transition: the transition from one occupied band to multiple occupied bands, and the abrupt change in the slope of lowest energy band with doping.