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

Abstract

We elucidate the general rule governing the response of dislocation lines in three-dimensional topological band insulators. According to this $\mathbf{K}\text{-}\mathbf{b}\text{-}\mathbf{t}$ rule, the lattice topology, represented by dislocation lines oriented in direction $\mathbf{t}$ with Burgers vector $\mathbf{b}$, combines with the electronic-band topology, characterized by the band-inversion momentum ${\mathbf{K}}_{\mathrm{inv}}$, to produce gapless propagating modes when the plane orthogonal to the dislocation line features a band inversion with a nontrivial ensuing flux $\Phi ={\mathbf{K}}_{\mathrm{inv}}\cdot \mathbf{b}(\mathrm{mod}2\pi )$. Although it has already been discovered by Y. Ran {\it et al.}, Nature Phys. {\bf 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 $\mathbf{K}\text{-}\mathbf{b}\text{-}\mathbf{t}$ rule . Finally, we discuss possible experimentally consequential examples in which the modes are oblivious for the direction of propagation, such as the recently proposed topologically-insulating state in electron-doped BaBiO${}_3$.

Main text + supplementary material, published version

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