Impact of Step Defects on Surface States of Topological Insulators

TL;DR

This paper provides an exact solution for surface states of topological insulators with step defects, revealing spin rotations and oscillation behaviors in local density of states that depend on defect orientation and energy.

Contribution

It offers a novel exact analytical approach to understanding how step defects influence surface states and spin textures in topological insulators.

Findings

Surface states exhibit spin rotations across step defects.

Oscillation periods in LDOS depend on defect orientation and bias voltage.

Results align qualitatively with recent STM observations.

Abstract

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.