Topological insulators: Theory & concepts

The spin-orbit interaction in condensed matter [1] is a key ingredient of contemporary approaches to spintronics [2,3]. 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 [4]. 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 [5,6]. In their 2D realization, topological insulators exhibit spin-polarized one-dimensional (1D) edge states [7], while the three-dimensional (3D) versions are characterized by 2D surface states with a spin-textured Dirac cone dispersion [8]. The inherent spin-texture of these electronic states provides a natural route toward 'topological spintronics' by generating an efficient spin-transfer torque [9,10].