Theory of Electron-Doped Ferroelectric Interfaces

We introduce and describe a self-consistent model for a ferroelectric interface that is doped via the polar catastrophe mechanism, as would be expected in LaAlO₃/Sr_1-xCa_xTiO₃ interfaces. We find that the resultant metallic state is characterized by the intertwining of lattice polarization and electronic degrees of freedom;  the electron gas binds to polarization gradients to form a compensated state with net vanishing charge density.  In this way, depolarizing fields are screened while external fields remain at least partly unscreened.  Thus, in contrast to naive expectations that the free electron gas screens external fields, we find S-shaped hysteretic polarization curves as a function of bias voltage.  We argue that switchable metallic films may be optimized by tuning the electron density to be slightly less than the lattice polarization; at higher electron densities, a fraction of the electron gas spills over to the interface and interferes with the switchability of the electronic state.  We find, in addition, a low-polarization state with a negative susceptibility that is due to the formation of a head-to-head domain wall.  This domain formation is enabled by the screening of depolarizing fields by the electron gas.