Spectroscopic Imaging Scanning Tunneling Microscopy as a Probe of Orbital Structures and Ordering

Unlike charge and spin, the orbital degree of freedom of electrons in transition metal oxides is difficult to detect. We present a theoretical study of a new detection method in metallic orbitally active systems by analyzing the quasiparticle scattering interference (QPI) pattern of the spectroscopic imaging scanning tunneling spectroscopy, which is sensitive to orbital structures and orbital ordering. The QPIs for the $d_{xz}$ and $d_{yz}$-orbital bands in the $t_{2g}$-orbital systems show a characteristic stripelike feature as a consequence of their quasi-one-dimensional nature, which is robust against orbital hybridization. With the occurrence of orbital ordering proposed in ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ and iron pnictides, the stripelike QPI patterns exhibit nematic distortion breaking the $C_4$ symmetry.

Figure 1

(a) The Fermi surfaces with an ideal quasi-1D bands without hybridization and (b) the corresponding FT-STM image. The stripe features in (b) at $q_x=0$ and $q_y=0$ result from the quasiparticle scatterings indicated by arrows within the same lines in (a), and those appearing at $q_x=\pm 2k_F$ and $q_y=\pm 2k_F$ come from scatterings indicated by arrows between different lines in (a), echoing the Friedel oscillation in exact 1D case.

Figure 2

Fermi surfaces (dashed lines) of the two quasi-1D bands at energies (a) just below the vH singularity ($E=1.8$) and (c) just above the vH singularity ($E=2.0$). The corresponding FT-STM images are presented in (b) and (d). The background gray scale in (a) and (c) represents the values of ${\theta }_{\overrightarrow{k}}$, exhibiting from white to dark gray for ${\theta }_{\overrightarrow{k}}=0\to \frac{\pi }{2}$. The scatterings between two $\overrightarrow{k}$ points in areas with different colors (indicated by the solid arrows) are strongly suppressed. The striped pattern disappears and discrete QPI wave vector points become dominant when the Fermi surface breaks down to discrete segments. The dashed arrows in (a) and (c) refer to the scatterings responsible for the strongest features in the FT-STM images.

Figure 3

(a) Fermi surface and (b) FT-STM image of the two quasi-1D band model for ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ with nematic order right at the van Hove singularity ($E=1.9$).