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

Abstract

Topological band-insulators (TBIs) represent a new class of quantum materials that in the presence of time-reversal symmetry (TRS) feature an insulating bulk bandgap together with metallic edge or surface states protected by a Z 2 topological invariant [1,2,3,4]. Recently, an extra layer in this Z 2 classification of TBIs has been uncovered by considering the crystal symmetries [5]. Dislocation lines being the unique topological defects related to the lattice translations play a fundamental role in this endeavor. We here elucidate the general rule governing their response in three-dimensional TBIs and uncover their role in this classification. According to that K-b-t rule, the lattice topology, represented by dislocation lines oriented in the direction t with the Burgers vector b , conspires with the electronic-band topology, characterized by the band-inversion momentum K inv , to produce gapless propagating modes along these line defects, which were discovered in Ref. [6]. For sufficiently symmetric crystals, this conspiracy leads to the topologically-protected metallic states inside the dislocation loops, which could also be important for applications. Finally, these findings are experimentally consequential as dislocation defects are ubiquitous in the real crystals.