The Space Group Classification of Topological Band Insulators

Abstract

[evdate 2012-12-17] IAS Symposium on Frontiers in Condensed Matter Physics. Talk no.4 Title from title slide.

Abstract: The existing classification for topological band insulators (TBI's) departs from time reversal symmetry but the role of the crystal lattice symmetries remained elusive. The speaker discovered a classification for TBI's, which we believe is complete, based on both time reversal as well as the symmetries of the ionic lattice. In this classification, the TBI's protected by time reversal fall in two subclasses: the 'Gamma type' and the 'translationally active' TBI's where the latter are destroyed by crystalline topological disorder (dislocations). In addition, the speaker identify 'valley' or 'crystalline' TBI's which are exclusively protected by lattice symmetries, where the 'weak' 3D TBI's form a subclass only protected by 2D point group symmetries. The talk propose a general system of indices to characterize all TBI's based on space-group classification. We show that there are 17 thermodynamically different TBI's in 2D and more than 70 in 3D.

Duration: 44 min.