Spectroscopic signatures of molecular orbitals in transition metal oxides with a honeycomb lattice

A tendency to form benzenelike molecular orbitals has recently been shown to be a common feature of the $4d$ and $5d$ transition metal oxides with a honeycomb lattice. This tendency competes with other interactions such as the spin-orbit coupling and Hubbard correlations and can be partially or completely suppressed. In the calculations, ${\mathrm{SrRu}}_2{\mathrm{O}}_6$ presents the cleanest case of well-formed molecular orbitals so far; however, direct experimental evidence for or against this proposition has been missing. In this paper, we show that combined photoemission and optical studies can be used to identify molecular orbitals in ${\mathrm{SrRu}}_2{\mathrm{O}}_6$. Symmetry-driven election selection rules suppress optical transitions between certain molecular orbitals, while photoemission and inverse photoemission measurements are insensitive to them. Comparing the photoemission and optical conductivity spectra, one should be able to observe clear signatures of molecular orbitals.

Figure 1

The projection of the crystal structure of ${\mathrm{SrRu}}_2{\mathrm{O}}_6$ onto the $ab$ plane. The black line indicates the unit cell boundary.

Figure 2

The nonmagnetic GGA band structure (top panel) and total DOS obtained by GGA calculation for the Neél antiferromagnetic structure (bottom panel). The contributions from different molecular orbitals are labeled according to Refs. [8, 12].

Figure 3

Results of the antiferromagnetic GGA calculations. (a) The joint density of states $J\left(\omega \right)$ is shown by black line. (b) The real part of the optical conductivity, $\mathrm{Re}{\sigma }_{\alpha \beta }\left(\omega \right)=\frac{\omega }{4\pi }\mathrm{Im}{\varepsilon }_{\alpha \beta }\left(\omega \right)$, where $\alpha ,\beta =x$ (blue dashed line) and $\alpha ,\beta =z$ (green dashed line). The imaginary part of the frequency-dependent dielectric functions (c) ${\varepsilon }_{xx}$ and (d) ${\varepsilon }_{zz}$.

Figure 4

The effective number of electrons obtained for ${\mathrm{SrRu}}_2{\mathrm{O}}_6$ in the GGA calculation according to Eq. (10) for the ${\varepsilon }_{xx}$ component.