Impact of Step Defect on Surface States of Topological Insulators

Recent topological insulators have attracted much attention in the condensed matter community due to the existence of surface states. The Dirac-cone topological surface states, which preserve time-reversal symmetry, are produced by strong spin- orbit coupling. In recent STM experiments, the modulations of local density of states (LDOS) induced by a step defect were observed. In this work, we investigate electron tunneling in the presence of $\delta(x)$ or $\delta(y)$ potential on the surface of topological insulators in the framework of quantum mechanics and calculate the LDOS near the $\delta $ potential. The STM experiments could be interpreted by an additional spin torque term in the wave function. We also figure out the oscillatory features of the LDOS produced by the $\delta(x)$ and $\delta(y)$ potentials, respectively.