Quantum singularity in topological insulators

Dislocations in the three-dimensional topological insulator have a similar effect as a hole threading magnetic flux. In this study, we have analytically considered a dislocation in three-dimensional topological insulator using the Dirac and the modified Dirac equation. A quantum singularity that originated in the dislocation creates a defect in momentum space. This defect relates to a phase transition and causes topologically protected zero-energy mode bound to the quantum singularity.