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⁡(mod⁡2⁢𝜋). 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.