High-carrier-density phase in LaTiO$_{3}$/SrTiO$_{3}$ superlattices

We investigate superlattices composed of alternating layers of Mott insulating LaTiO$_{3}$ and band insulating SrTiO$_{3}$ from first principles, using the density functional theory plus U (DFT+U) method. For values of U above a critical threshold, we find that melting of the Mott-insulating phase can extend from the interface into the LaTiO$_{3}$ layer, resulting in a sheet carrier density exceeding the density of 0.5 electrons per in-plane unit cell found in previous studies. The critical U for the melting transition is larger than the critical Coulomb correlation required for the insulating LaTiO$_{3}$, suggesting the existence of a high sheet carrier density phase in LaTiO$_{3}$/SrTiO$_{3}$ superlattices. The effects of in-plane strain and varying layer thickness on the melting transition are discussed. For insulating superlattices, we study the strain and thickness dependence of the polarization and its relation to near-interface local atomic distortions.