The eigenstates in the presence of a step defect (SD) along the $x$ or $y$ axis on the surface of topological insulators are exactly solved. It is shown that unlike the electronic states in conventional metals, the topological surface states across the SD can produce spin rotations. The magnitudes of the spin rotations depend on the height and direction of the SD. The oscillations of local density of states (LDOS) are characterized by a wave vector connecting two points on the hexagonal constant-energy contour at higher energies. The period of the oscillation caused by the SD along the $y$ axis is $\sqrt{3}$ ($\frac{1}{\sqrt{3}}$) times that induced by the SD along the $x$ axis at a larger positive (negative) bias voltage. With increasing the bias voltage, the period of the oscillation, insensitive to the strength of the SD, becomes smaller. At lower energies near the Fermi surface, the two types of wave vectors coexist in the LDOS modulations. These results are consistent qualitatively with recent observations of scanning tunneling microscopy.

• Received 10 October 2011

DOI:https://doi.org/10.1103/PhysRevB.85.115434