Band Structure and Terahertz Optical Conductivity of Transition Metal Oxides: Theory and Application to ${\mathrm{CaRuO}}_3$

Density functional plus dynamical mean field calculations are used to show that in transition metal oxides, rotational and tilting (${\mathrm{GdFeO}}_3$-type) distortions of the ideal cubic perovskite structure produce a multiplicity of low-energy optical transitions which affect the conductivity down to frequencies of the order of 1 or 2 mV (terahertz regime), mimicking non-Fermi-liquid effects even in systems with a strictly Fermi-liquid self-energy. For ${\mathrm{CaRuO}}_3$, a material whose measured electromagnetic response in the terahertz frequency regime has been interpreted as evidence for non-Fermi-liquid physics, the combination of these band structure effects and a renormalized Fermi-liquid self-energy accounts for the low frequency optical response which had previously been regarded as a signature of exotic physics. Signatures of deviations from Fermi-liquid behavior at higher frequencies ($\sim 100\mathrm{meV}$) are discussed.

Figure 1

(Main panel) Optical conductivity (normalized to its zero frequency value). (Heavy solid blue line) Conductivity computed from $\mathrm{DFT}+\mathrm{DMFT}$ at $T=30\mathrm{K}$ for the orthorhombic experimental structure. The dashed straight line is a guide to the eye indicating the power-law behavior $\sim {\omega }^{-0.5}$, corresponding to the experimentally reported mid-IR frequency dependence [1]. Also displayed are the conductivities computed for a hypothetical cubic structure (intermediate weight red line) and from the Allen formula (light black line), using the same DMFT self-energy as was used in the experimental structure calculation. Finally, the dotted line presents the “SBFL” result obtained by using a Fermi-liquid self-energy in the Allen formula. [Inset (a)] Optical conductivity calculated using DMFT self-energy for experimental structure and cubic structure compared to a calculation (dashed lines) for the experimental structure but with a Fermi-liquid self-energy [Eq. (4)]. [Inset (b)] Experimental data of Ref. [4] in the terahertz range along with the DMFT calculation for the realistic structure.

Figure 2

Band structure computed for (a) the ideal cubic perovskite form of ${\mathrm{CaRuO}}_3$ plotted along high symmetry directions in the cubic perovskite Brillouin zone; (b) the ideal cubic structure folded back into the Brillouin zone of the experimental orthorhombic structure; and (c) the experimental orthorhombic structure, along high symmetry directions of the orthorhombic Brillouin zone. All three panels show the frontier $t_{2g}$-antibonding bands produced by a MLWF fitting of the DFT (generalized gradient approximation) band structure. (Inset) Optical transitions across minigaps which are forbidden in the cubic structure are activated in the distorted structure.

Figure 3

(a) Real part of the self-energy for one of the three orbitals (solid line). (Dash-dotted line) Linear low frequency fit to the real part of Eq. (4) with slope $1-Z^{-1}\equiv d\mathrm{\Sigma }/d\omega =-5.3$. (b) Imaginary part of self-energy of the same orbital (solid line). (Dash-dotted line) Low-energy Fermi-liquid fit to the imaginary part of Eq. (4) with ${\mathrm{\Omega }}_0\simeq 14\mathrm{meV}$ and temperature $T=0.0025\mathrm{meV}\approx 30\mathrm{K}$. (Vertical lines) Boundary of the Fermi-liquid region ($\omega =0.09\mathrm{eV}$).

Figure 4

Optical mass (a) and scattering rate (b) obtained via Eq. (5) for different cases considered in this Letter and compared to quasiparticle mass [$\sim 6.7$, as calculated from the slope of $\mathrm{Im}\mathrm{\Sigma }(i{\omega }_n)$] and the imaginary part of the single particle self-energy (dashed green curve). Dotted magenta curves indicate ${\omega }^{\pm 0.5}$ behavior.