Topological Insulators from Group Cohomology

Topological Gauge Theories and Group Cohomology

We show that three dimensional Chern-Simons gauge theories with a compact gauge group G (not necessarily connected or simply connected) can be classified by the integer cohomology group H(BG,Z). In a similar way, possible Wess-Zumino interactions of such a group G are classified by H(G, Z). The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involve...

Topological insulators

Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials

In this review, we discuss recent progress in the explorations of topological materials beyond topological insulators; specifically, we focus on topological crystalline insulators and bulk topological superconductors. The basic concepts, model Hamiltonians, and novel electronic properties of these new topological materials are explained. The key role of symmetries that underlie their topologica...

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...

Topological Insulators and Superconductors

We study theoretical properties of robust low energy electronic excitations associated with topological insulators and superconductors. The bulk materials are described by non-interacting single particle band Hamiltonians with a finite excitation gap. Their topological phases are classifed according to symmetries and dimensions, characterized by discrete bulk invariants, and correspond to topol...