Effects of spin-orbit interaction and electron correlations in strontium titanate

We show that the Bloch states in conduction band of SrTiO$_3$ arise from interplay between highly anisotropic hopping sub-bands derived Ti $t_{2g}$ orbitals and spin-orbit coupling mixes these orbitals. Because nearly flat-band characteristics for one principal axes, at sufficiently high doping become unstable with respect to electron interactions, resulting Mott-like singlet correlations. These findings may be relevant anomalous electronic properties SrTiO$_3$, including its unusual superconductivity.