  The effects of lattice relaxation in LaTiO$_3$/SrTiO$_3$ superlattices are
investigated using a combination of LDA$+U$ density functional theory, and
Hartree-Fock effective Hamiltonian calculations. We find noticeable ($\sim
0.1$--0.2 \AA) distortions of the TiO$_6$ octahedra in the near-La region. The
resulting screening changes the Ti $d$-electron density substantially.
Tight-binding fits to the relaxed-lattice band structure, combined with
Hartree-Fock calculations of the resulting model, reveal a novel phase with
$xy$ orbital order, which does not occur in bulk LaTiO$_3$, or in the
hypothetical unrelaxed structure.
