Impact of electric-field dependent dielectric constants on two-dimensional electron gases in complex oxides

High-density two-dimensional electron gas (2DEG) can be formed at complex oxide interfaces such as SrTiO₃/GdTiO₃ and SrTiO₃/LaAlO₃. The electric field in the vicinity of the interface depends on the dielectric properties of the material as well as on the electron distribution. However, it is known that electric fields can strongly modify the dielectric constant of SrTiO₃ as well as other complex oxides. Solving the electrostatic problem thus requires a self-consistent approach in which the dielectric constant varies according to the local magnitude of the field. We have implemented the field dependence of the dielectric constant in a Schrödinger-Poisson solver in order to study its effect on the electron distribution in a 2DEG. Using the SrTiO₃/GdTiO₃ interface as an example, we demonstrate that including the field dependence results in the 2DEG being confined closer to the interface compared to assuming a single field-independent value for the dielectric constant. Our conclusions also apply to SrTiO₃/LaAlO₃ as well as other similar interfaces.