A-geometrical approach to topological insulators with edge dislocations

A study of the propagation of electrons with varying spinor orientability is conducted using the coordinate transformation method. Topological insulators are characterized by an odd number of changes in the orientability of the spinors in the Brillouin zone. For defects the change in spinor orientability takes place for closed orbits in real space. Both the cases are characterized by nontrivial spin connections. Using this method we derive the form of the spin connections for topological defects in three-dimensional (3D) topological insulators. On the surface of a topological insulator, the presence of an edge dislocation gives rise to a spin connection controlled by torsion. We find that electrons propagate along 2D regions and confined circular contours. We compute for the edge dislocations the tunneling density of states. The edge dislocations violate parity symmetry, resulting in a current measured by the in-plane component of the spin on the surface. For a continuum distribution of edge dislocations with the Burger vector B⁽²⁾ in the y-direction, we show that electron backscattering is absent for electrons with zero momentum in the y-direction.