  The eigenstates in the presence of a step defect (SD) along $x$ 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 y axis is $\sqrt 3$
($\frac{1}{\sqrt 3}$) times that induced by the SD along 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.
