Within the last twenty years, the status of the spinorbit interaction has evolved from that of a simple atomic contribution to a key effect that modifies the electronic band structure of materials. It is regarded as one of the basic ingredients for spintronics, locking together charge and spin degrees of freedom and recently it is instrumental in promoting a new class of compounds, the topological insulators. In this review, we present the current status of the research on the spinorbit coupling in transition metal oxides, discussing the case of two semiconducting compounds, SrTiO₃and KTaO₃, and the properties of surface and interfaces based on these. We conclude with the investigation of topological effects predicted to occur in different complex oxides.

Quantum confinement at complex oxide interfaces establishes an intricate hierarchy of the strongly correlated d orbitals which is widely recognized as a source of emergent physics. The most prominent example is the (001) LaAlO3/SrTiO3 (LAO/STO) interface, which features a dome-shaped phase diagram of superconducting critical temperature and spin-orbit coupling (SOC) as a function of electrostatic doping, arising from a selective occupancy of t2g orbitals of different character. Here we study (111)-oriented LAO/STO interfaces, where the three t2g orbitals contribute equally to the subband states caused by confinement, and investigate the impact of this unique feature on electronic transport. We show that transport occurs through two sets of electronlike subbands, and the carrier density of one of the sets shows a nonmonotonic dependence on the sample conductance. Using tight-binding modeling, we demonstrate that this behavior stems from a band inversion driven by on-site Coulomb interactions. The balanced contribution of all t2g orbitals to electronic transport is shown to result in strong SOC with reduced electrostatic modulation.

We explore the superconducting phase diagram of the two-dimensional electron system at the LaAlO3/SrTiO3 interface by monitoring the frequencies of the cavity modes of a coplanar waveguide resonator fabricated in the interface itself. We determine the phase diagram of the superconducting transition as a function of the temperature and electrostatic gating, finding that both the superfluid density and the transition temperature follow a dome shape but that the two are not monotonically related. The ground state of this two-dimensional electron system is interpreted as a Josephson junction array, where a transition from long- to short-range order occurs as a function of the electronic doping. The synergy between correlated oxides and superconducting circuits is revealed to be a promising route to investigate these exotic compounds, complementary to standard magnetotransport measurements.

We investigate the thickness-dependent electronic properties of ultrathin SrIrO3 and discover a transition from a semimetallic to a correlated insulating state below 4 unit cells. Low-temperature magnetoconductance measurements show that spin fluctuations in the semimetallic state are significantly enhanced while approaching the transition point. The electronic properties are further studied by scanning tunneling spectroscopy, showing that 4 unit cell SrIrO3 is on the verge of a gap opening. Our density functional theory calculations reproduce the critical thickness of the transition and show that the opening of a gap in ultrathin SrIrO3 requires antiferromagnetic order.