Weak topological insulator with protected gapless helical states

A workable model for describing dislocation lines introduced into a three-dimensional topological insulator is proposed. We show how fragile surface Dirac cones of a weak topological insulator evolve into protected gapless helical modes confined to the vicinity of a dislocation line. It is demonstrated that surface Dirac cones of a topological insulator (either strong or weak) acquire a finite-size energy gap when the surface is deformed into a cylinder penetrating the otherwise surfaceless system. We show that, when a dislocation with a nontrivial Burgers vector is introduced, the finite-size energy gap plays the role of stabilizing the one-dimensional gapless states.