Colloquium: Topological insulators

Topological insulators are electronic materials that have a bulk band gap\nlike an ordinary insulator, but have protected conducting states on their edge\nor surface. The 2D topological insulator is a quantum spin Hall insulator,\nwhich is a close cousin of the integer quantum Hall state. A 3D topological\ninsulator supports novel spin polarized 2D Dirac fermions on its surface. In\nthis Colloquium article we will review the theoretical foundation for these\nelectronic states and describe recent experiments in which their signatures\nhave been observed. We will describe transport experiments on HgCdTe quantum\nwells that demonstrate the existence of the edge states predicted for the\nquantum spin Hall insulator. We will then discuss experiments on Bi_{1-x}Sb_x,\nBi_2 Se_3, Bi_2 Te_3 and Sb_2 Te_3 that establish these materials as 3D\ntopological insulators and directly probe the topology of their surface states.\nWe will then describe exotic states that can occur at the surface of a 3D\ntopological insulator due to an induced energy gap. A magnetic gap leads to a\nnovel quantum Hall state that gives rise to a topological magnetoelectric\neffect. A superconducting energy gap leads to a state that supports Majorana\nfermions, and may provide a new venue for realizing proposals for topological\nquantum computation. We will close by discussing prospects for observing these\nexotic states, a well as other potential device applications of topological\ninsulators.\n