Topological field theories of three-dimensional rotation symmetric insulators: Coupling curvature and electromagnetism

Three-Dimensional Topological Insulators

Topological insulators in three dimensions are nonmagnetic insulators that possess metallic surface states (SSs) as a consequence of the nontrivial topology of electronic wavefunctions in the bulk of the material. They are the first known examples of topological order in bulk solids. We review the basic phenomena and experimental history, starting with the observation of topological insulator b...

Topological Field Theories associated with Three Dimensional Seiberg-Witten Monopoles

Three dimensional topological field theories associated with the three dimensional version of Abelian and non-Abelian Seiberg-Witten monopoles are presented. These three dimensional monopole equations are obtained by a dimensional reduction of the four dimensional ones. The starting actions to be considered are Gaussian types with random auxiliary fields. As the local gauge symmetries with topo...

Curvature relations in three-dimensional symmetric axes

Aspects of symmetric axis geometry in three dimensions are discussed. A notion of radius curvature is defined and a relationship between symmetric axis curvature, radius curvature, and boundary curvature is derived.

Interacting Surface States of Three-Dimensional Topological Insulators.

We numerically investigate the surface states of a strong topological insulator in the presence of strong electron-electron interactions. We choose a spherical topological insulator geometry to make the surface amenable to a finite size analysis. The single-particle problem maps to that of Landau orbitals on the sphere with a magnetic monopole at the center that has unit strength and opposite s...

On 2-dimensional Topological Field Theories