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 the 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 stripe-like feature as a consequence of their quasi-one-dimensional nature, which is robust against orbital hybridization. With the occurrence of orbital ordering proposed in Sr$_3$Ru$_2$O$_7$ and iron-pnictides, the stripe-like QPI patterns exhibit nematic distortion breaking the $C_4$-symmetry.