The two dimensional local density of states of a Topological Insulator with an edge dislocation

We investigate the effect of a crystal edge dislocation on the metallic surface of a Topological Insulator. The edge dislocation gives rise to torsion which the electrons experience as a spin connection. As a result the electrons propagate along confined two dimensional regions and circular contours. Due to the edge dislocations the parity symmetry is violated resulting in a current measured by the in-plane component of the spin on the surface. The tunneling density of states for Burger vectors in the $y$ direction is maximal along the $x$ direction. The evidence of the enhanced tunneling density of states can be verified with the help of the scanning tunneling technique.