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arXiv:1910.04151 [cond-mat.mes-hall]AbstractReferencesReviewsResources

Type-II quadrupole topological insulators

Yan-Bin Yang, Kai Li, L. -M. Duan, Yong Xu

Published 2019-10-09Version 1

Modern theory of electric polarization is formulated by the Berry phase, which, when quantized, leads to topological phases of matter. Such a formulation has recently been extended to higher electric multipole moments, through the discovery of the so-called quadupole topological insulator. It has been established by a classical electromagnetic theory that in a two-dimensional material the quantized properties for the quadupole topological insulator should satisfy a basic relation. Here we discover a new type of quadupole topological insulator (dubbed as type-II) that violates this relation due to the breakdown of a previously established theory that a Wannier band and an edge energy spectrum are topologically equivalent in a closed quantum system. We find that, similar to the previously discovered (referred to as type-I) quadrupole topological insulator, the type-II hosts topologically protected corner states carrying fractional corner charges. However, the edge polarizations only occur at a pair of boundaries in the type-II insulating phase, leading to the violation of the classical constraint. We propose an experimental scheme to realize such a new topological phase of matter. The existence of the new topological insulating phase means that new multipole topological insulators with distinct properties can exist in broader contexts beyond classical constraints.