C. L. Kane

Colloquium : Topological Insulators

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to the combination of spin-orbit 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 Hall state. A three-dimensional (3D) topological insulator supports novel spin-polarized 2D Dirac fermions on its surface. In this Colloquium the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topological insulators have been observed. Transport experiments on

Quantum Spin Hall Effect in Graphene

\mathrm{Hg}\mathrm{Te}∕\mathrm{Cd}\mathrm{Te}

Z-2 Topological Order and the Quantum Spin Hall Effect

quantum wells are described that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. Experiments on

High-field electrical transport in single-wall carbon nanotubes

{\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}

Size, Shape, and Low Energy Electronic Structure of Carbon Nanotubes

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Observation of Unconventional Quantum Spin Textures in Topological Insulators

{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}

Dirac semimetal in three dimensions.

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Coulomb Interactions and Mesoscopic Effects in Carbon Nanotubes

{\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}

Probing Neutral Majorana Fermion Edge Modes with Charge Transport

, and

Dirac Line Nodes in Inversion-Symmetric Crystals

{\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}