Oxide heterostructures are of great interest both for fundamental and applicative reasons. In particular the two-dimensional electron gas at the LaAlO$_3$/SrTiO$_3$ or LaTiO$_3$/SrTiO$_3$ interfaces displays many different physical properties and fun
ctionalities. However there are clear indications that the interface electronic state is strongly inhomogeneous and therefore it is crucially relevant to investigate possible intrinsic electronic mechanisms underlying this inhomogeneity. Here the electrostatic potential confining the electron gas at the interface is calculated self-consistently, finding that the electron confinement at the interface may induce phase separation, to avoid a thermodynamically unstable state with a negative compressibility. This provides a generic robust and intrinsic mechanism for the experimentally observed inhomogeneous character of these interfaces.
Several experiments reveal the inhomogeneous character of the superconducting state that occurs when the carrier density of the two-dimensional electron gas formed at the LaXO3/SrTiO3 (X=Al or Ti) interface is tuned above a threshold value by means o
f gating. Re-analyzing previous measurements, that highlight the presence of two kinds of carriers, with low and high mobility, we shall provide a description of multi-carrier magneto-transport in an inhomogeneous two-dimensional electron gas, gaining insight into the properties of the physics of the systems under investigation. We shall then show that the measured resistance, superfluid density, and tunneling spectra result from the percolative connection of superconducting puddles with randomly distributed critical temperatures, embedded in a weakly localizing metallic matrix. We shall also show that this scenario is consistent with the characteristics of the superconductor-to-metal transition driven by a magnetic field. A multi-carrier description of the superconducting state, within a weak-coupling BCS-like model, will be finally discussed.
We propose a model for the two-dimensional electron gas formed at the interface of oxide heterostructures that includes a Rashba spin-orbit coupling proportional to an electric field oriented perpendicularly to the interface. Taking into account the
electron density dependence of this electric field confining the electron gas at the interface, we report the occurrence of a phase separation instability (signaled by a negative compressibility) for realistic values of the spin-orbit coupling and of the electronic band-structure parameters at zero temperature. We extend the analysis to finite temperatures and in the presence of an in-plane magnetic field, thereby obtaining two phase diagrams which exhibit a phase separation dome. By varying the gating potential the phase separation dome may shrink and vanish at zero temperature into a quantum critical point where the charge fluctuates dynamically. Similarly the phase separation may be spoiled by a planar magnetic field even at zero temperature leading to a line of quantum critical points.
