Pseudogap Dependence of the Optical Conductivity Spectra of ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$: A Possible Contribution of the Orbital Flip Excitation

Optical spectra of a double-layered perovskite ruthenate ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ show a pseudogap opening around $200{\mathrm{cm}}^{-1}$ below 50 K, which is attributable to the partial $k$-space gap opening due to the density wave instability. Unlike most other density wave materials, ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ has spectral weight redistributions, not near the energy gap region, but at a much higher energy region around $800{\mathrm{cm}}^{-1}$. As a possible origin of these intriguing features, we discuss the orbital flip excitation in the density wave ground state.

Figure 1

The $ab$ plane $R(\omega )$ of ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ at 50 K and 10 K. $R(\omega )$ at 10 K shows a diplike suppression around $100{\mathrm{cm}}^{-1}$. The inset shows a $T$-dependent dc resistivity below 300 K.

Figure 2

(a) The far-infrared $ab$ plane $\sigma (\omega )$ of ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$. Below 50 K, the PG opens around $200{\mathrm{cm}}^{-1}$ and a narrow Drude-like peak appears inside the PG energy. The spectral part below $12{\mathrm{cm}}^{-1}$, which is the lowest frequency of the experimental data, is displayed with the dotted lines. $T$ dependences of several parameters related to the coherent peak, i.e., ${\omega }_p^2$ and $1/\tau$ (b), and the gap feature, i.e., $E_G(T)/E_G(10\mathrm{K})$ and $\Delta SW$ (c).

Figure 3

Schematic diagrams of the spectral weight change of the BCS-type gap state for the coherent factor in case I (a) and case II (b). ${\sigma }_n(\omega )$ represents the $\sigma (\omega )$ of the normal state. The solid lines in each figure correspond to the curves at 0 K. (c) A schematic diagram of the spectral weight redistribution for ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ with the density wave gap opening. The inset shows the spin-orbital configuration at the ground state of ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ and the orbital flip excitation. The sinusoidal curve (red color) represents a modulation of charge or spin degree of freedom related to the density wave instability for the $d_{yz}$ orbital state. The orbital flip excitation provides a strong perturbation to such modulation, as depicted as the broken curve.

Figure 4

The $ab$ plane $\sigma (\omega )$ of ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ up to $2500{\mathrm{cm}}^{-1}$. Accompanying the PG opening at $T<50\mathrm{K}$, the spectral weight of the midinfrared peak around $800{\mathrm{cm}}^{-1}$ increases. The sharp spike around $600{\mathrm{cm}}^{-1}$ is due to the infrared-active phonon mode. The inset shows the $\sigma (\omega )$ up to $12500{\mathrm{cm}}^{-1}$, where the spectral weight around $8000{\mathrm{cm}}^{-1}$ decreases as $T$ decreases.