Octahedral distortions in SrNbO$_3$: Unraveling the structure-property relation

Strontium niobate has triggered a lot of interest as a transparent conductor and as a possible realization of a correlated Dirac semi-metal. Using the lattice parameters as a tunable knob, the energy landscape of octahedral tilting was mapped using density functional theory calculations. We find that biaxial compressive strain induces tilting around the out-of-plane axis, while tensile strain induces tilting around the two in-plane axes. The two competing distorted structures for compressive strain show semi-Dirac dispersions above the Fermi level in their electronic structure. Our density functional theory calculations combined with dynamical mean field theory (DFT+DMFT) reveals that dynamical correlations downshift these semi-Dirac like cones towards the Fermi energy. More generally, our study reveals that the competition between the in-phase and out-of-phase tilting in SrNbO$_3$ provides a new degree of freedom which allows for tuning the thermoelectric and optical properties. We show how the tilt angle and mode is reflected in the behavior of the Seebeck coefficient and the plasma frequency, due to changes in the band structure.