Topological insulators: Theory & concepts

The spin-orbit interaction in condensed matter is a key ingredient of contemporary approaches to spintronics. These approaches have primarily focused on the “interior” bulk electronic states of semiconductors and metals with parabolic energy-momentum dispersion. Early theoretical work however showed that in narrow band gap semiconductor heterostructures (derived from (Pb, Sn)Te and (Hg, Cd)Te), the spin-orbit interaction can lead to helical two dimensional (2D) interface states with a massless (linear) Dirac dispersion. Over the past 5 years or so, we have witnessed a rebirth of these concepts in the more contemporary context of “topological insulators,” driven by the recognition of deep and fundamental connections between surface or edge states and topological invariants. In their 2D realization, topological insulators exhibit spin-polarized one-dimensional (1D) edge states, while the three-dimensional (3D) versions are characterized by 2D surface states with a spin-textured Dirac cone dispersion. The inherent spin-texture of these electronic states provides a natural route toward “topological spintronics” by generating an efficient spin-transfer torque.