Higher-order topological Anderson insulators

Topological order parameters for interacting topological insulators.

We propose a topological order parameter for interacting topological insulators, expressed in terms of the full Green's functions of the interacting system. We show that it is exactly quantized for a time-reversal invariant topological insulator, and it can be experimentally measured through the topological magneto-electric effect. This topological order parameter can be applied to both interac...

Sufficient Conditions for Topological Order in Insulators

– We prove the existence of low energy excitations in insulating systems at general filling factor under certain conditions, and discuss in which cases these may be identified as topological excitations. In the specific case of half-filling this proof provides a significantly shortened proof of the recent higher dimensional Lieb-Schultz-Mattis theorem. The classic 1961 result of Lieb, Schultz, ...

Topological insulators

Reflection-Symmetric Second-Order Topological Insulators and Superconductors.

Second-order topological insulators are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but with topologically protected gapless states at the intersection of two boundaries. Without further spatial symmetries, five of the ten Altland-Zirnbauer symmetry classes allow for the existence of such second-order topological insulators in two and three dimensions. We show t...

Topological crystalline insulators.

The recent discovery of topological insulators has revived interest in the band topology of insulators. In this Letter, we extend the topological classification of band structures to include certain crystal point group symmetry. We find a class of three-dimensional "topological crystalline insulators" which have metallic surface states with quadratic band degeneracy on high symmetry crystal sur...