Nonsymmorphic symmetry and helical dislocation modes in topological insulators and semimetals

A lattice dislocation in a topological insulator can trap one pair of helical electron modes as a response of nonzero weak Z2​ topological indices. For rotationally invariant systems, a screw dislocation locally reduces the symmetry to a nonsymmorphic screw rotation, allowing its eigenvalues to serve as an additional quantum label for the defect bound states. We show that this defect-induced nonsymmorphic symmetry can stabilize two or more pairs of helical dislocation modes, even in insulators or semimetals with trivial weak Z2​ indices. A classification of symmetry-protected helical dislocation modes will be discussed, along with minimal model systems where these exotic modes can emerge.