Condensed matter physics

In electron-doped ferroelectrics, the free electrons can become concentrated along the domain walls which act like a conducting surface. We consider the impact of free electrons occupying the t2g orbitals on the domain walls of an electron-doped perovskite ferroelectric. We build an analytical model based on Landau-Ginzburg-Devonshire theory, and a trio of tight-binding Hamiltonians for free electrons. We self-consistently solve for the polarization, potential, and electron density using a finite-difference approximation. We find that the ferroelectric is effectively charge neutral. The free electrons are attracted to the positively-charged domain wall, leaving it with a small residual charge. As the electron density increases, the domain walls tilt to form zig-zag domain walls. Orbital selectivity of the t2g orbitals depends on the relative orientations of the orbital plane and the domain wall. This property influences the rate at which the domain wall tilts as a function of the electron density.

Author Keywords: Charged Domain Wall, Domain Wall, Ferroelectric, Landau-Ginzburg, Perovskite, Strontium Titanate

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

S. Johri and R. Bhatt developed a real-space renormalization group approach aimed at extracting the localized single-particle eigenstates of the Anderson model from a large system by identifying clusters of resonant site potentials. E. Campbell generalized this real-space renormalization group approach using standard perturbation theory. Both approaches were intended to approximate the single-particle density of states of the Anderson model. In this thesis, we aimed to test the potential of applying a similar real-space renormalization group approach to calculate the density of states of the interacting Anderson-Hubbard model. Our interest in the density of states of this model is due to a V-shaped zero-bias anomaly in two-dimensional systems. A real-space renormalization group approach is best applied to a one-dimensional system. We found that the zero-bias anomaly is not V-shaped in one-dimension. To test the potential of a real-space renormalization group approach, we used the cluster approach which is the same as the non-interacting renormalization group approach but without the perturbation theory and found that for strong disorder this technique could accurately calculate the density of states over a wide range of energies but deviated from exact results at the band edge, at $\omega=\pm U$ and near $\omega=0$. The first two inaccuracies will be reduced with a proper real-space renormalization group approach. We suspect that the last inaccuracy is associated with long range physics and may be difficult to recover. We also developed a technique that adjusts the identification of clusters in the cluster approach to improve the computation time of the density of states with minimal loss of accuracy in a tunable range around the Fermi level. We found that this technique significantly reduced the computation time and was able to preserve the density of states near the Fermi level, except at the smallest energies near $\omega=0$.

Author Keywords: Anderson-Hubbard model, renormalization group, Strong electron correlations, Zero-bias anomaly

In 2004 it was discovered that a two-dimensional electron gas (2DEG) forms at the interface between lanthanum aluminate (LAO) and strontium titanate (STO). This 2DEG exhibits a variety of electronic and magnetic phenomena, motivating intense research into its applicability to electronic devices. Over the years several models have been developed in theoretical exploration of this system. Here, the transverse Ising model is applied to the LAO/STO interface for the first time. It is shown that the model as it is traditionally formulated cannot accurately predict the structure of the electron density at the interface. I show that this can be fixed with a simple modification of the model, and discuss how this modification affects both the polarization distribution in ferroelectric thin films and the electron density at the LAO/STO interface. The importance of including the depolarizing field when modelling spatially inhomogeneous ferroelectric systems is also explored.

Author Keywords: ferroelectric thin film, lanthanum aluminate, strontium titanate, transverse Ising model, two-dimensional electron gas

Many of the most interesting electronic behaviours currently being studied are associated with strong correlations. In addition, many of these materials are disordered either intrinsically or due to doping. Solving interacting systems exactly is extremely computationally expensive, and approximate techniques developed for strongly correlated systems are not easily adapted to include disorder. As a non-interacting disordered model, it makes sense to consider the Anderson model as a first step in developing an approximate method of solution to the interacting and disordered Anderson-Hubbard model. Our renormalization group (RG) approach is modeled on that proposed by Johri and Bhatt [23]. We found an error in their work which we have corrected in our procedure. After testing the execution of the RG, we benchmarked the density of states and inverse participation ratio results against exact diagonalization. Our approach is significantly faster than exact diagonalization and is most accurate in the limit of strong disorder.

Author Keywords: disorder, localization, real-space renormalization, strong correlations

Johri and Bhatt found singular behavior near the band edge in the density of states as well as in the inverse participation ratio of the Anderson model. These singularities mark a transition to an energy range dominated by resonant states. We study the interacting case using an ensemble of two-site Anderson-Hubbard systems. We find the ensemble-averaged density of states and generalized inverse participation ratio have more structure than in the non-interacting case because there are more transitions and in particular the transitions depend on the ground state. Nonetheless, there are regions of sharp decline in the generalized inverse participation ratio associated with specific density of state features. Moreover these features move closer to the Fermi level with the addition of interactions making them more experimentally accessible. Unfortunately resonances unique to interacting systems cannot be specifically identified.

Author Keywords: Correlated electrons, Disorder, Localization