Interplay between electronic topology and crystal symmetry: Dislocation-line modes in topological band insulators

We elucidate the general rule governing the response of dislocation lines in three-dimensional topological band insulators. According to this K-b-t rule, the lattice topology, represented by dislocation lines oriented in direction t with Burgers vector b, combines with the electronic-band topology, characterized by the band-inversion momentum Kᵢₙᵥ, to produce gapless propagating modes when the plane orthogonal to the dislocation line features a band inversion with a nontrivial ensuing flux Φ=Kᵢₙᵥ·b(mod0.16em0ex2π). Although it has already been discovered by Ran et al. [Nat. Phys. 5, 298 (2009)] that dislocation lines host propagating modes, the exact mechanism of their appearance in conjunction with the crystal symmetries of a topological state is provided by the K-b-t rule. Finally, we discuss possible experimentally consequential examples in which the modes are oblivious to the direction of propagation, such as the recently proposed topologically insulating state in electron-doped BaBiO₃.