Colloquium: Topological insulators

Colloquium: Topological Insulators

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducted states on their edge or surface. These states are possible due to the combination of spinorbit interactions and time-reversal symmetry. The two-dimensional (2D) topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hal...

Topological insulators

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...

Modulated Floquet topological insulators.

The application of spatially uniform light on conventional insulators can induce Floquet spectra with characteristics akin to those of topological insulators. We demonstrate that spatial modulation of light allows for remarkable control of the properties in these systems. We provide configurations to generate one-dimensional bulk modes, photoinduced currents, as well as fractionalized excitatio...