Charge density distribution and optical response of the LaAlO3/SrTiO3 interface

We present calculations of the charge density profile, subband occupancy, and ellipsometry spectra of the electron gas at the LaAlO₃/SrTiO₃ interface. The calculations employ self-consistent Hartree and random phase approximations, a tight-binding parametrization of the band structure, and a model for the optical phonon of SrTiO₃. The dependence of the spatial structure and occupancy of subbands on the magnitude of the polarization charge at the interface and the dielectric function is determined. The interface-confined subbands may be labeled by the symmetry (xy, xz, or yz) of the Ti d orbitals from which they mainly derive. The xy-derived band nearest the interface contains the major proportion of the electronic charge, but a large number of more distant, slightly occupied xy-derived bands are also found. Depending on the magnitude of the polarization charge, zero, one, or two xz/yz-derived subbands are found. When present, these xz/yz bands give the dominant contribution to the long-distance tail of the interface charge. The response to applied ac electric fields polarized parallel and perpendicular to the interface is calculated and the results are presented in terms of ellipsometry angles. Two features are found: a dip in the spectrum near the longitudinal optic (LO) feature of the SrTiO₃ phonon and a peak at the higher energy. We show that the form and magnitude of the dip are related to the Drude response of carriers moving in the plane of the interface, while the peak arises from the plasmon excitation of the xz and yz electrons. The relation of the features of the subband occupancies and the in-plane conductivities is given.