  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
labelled 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 LO feature of the STO phonon and a peak
at the higher energy. We show that the form and magnitude of the dip is 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.
