Topological insulators
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Introduction Topological insulators (TIs), discovered in the past decade, represent a new state of matter. TI materials have an insulating gap in the bulk and robust metallic edge/surface states on the surface.1–11 The topology for most insulators and semiconductors is trivial. Relativistic effects are the origin of the topologically non-trivial electronic structure, and as a consequence, most TIs contain heavy elements such as bismuth, platinum, or tellurium. TIs have been realized in both twodimensional thin films and three-dimensional bulk crystals. In both two and three dimensions, the surface states of TIs are “helical,” which means the spin of the surface state electron is locked in the direction of its velocity, as illustrated in Figure 1. As a consequence of this helical property, elastic backscattering of the surface state is completely suppressed as long as time-reversal symmetry is preserved. Due to the timereversal symmetry, back-scattering processes with clockwise and counter-clockwise spin rotation always have the same amplitude and opposite sign, which thus intefere destructively and result in perfect transmission of electrons.1 Additionally, this property guarantees the robustness of the surface states against disorder and leads to unique spin and charge transport properties of TIs. In particular, the edge state of twodimensional TIs carries a unidirectional spin current, which is why the two-dimensional TI is also known as the quantum spin Hall (QSH) state.
The discovery of TIs has led to a paradigm shift in condensed matter physics on two levels: (1) TI is a new state of quantum matter that enables the development of new technologies. (2) The dissipationless transport of the surface states can enable low power electronics applications. Additionally, it is the first successful example of the predictive power of theory in material science.
Materials and their properties Many different experimental techniques have been applied to study TI materials, including transport measurements, angle-resolved photo-emission spectroscopy (ARPES), scanning tunneling microscopy (STM), and optical conductivity. For three-dimensional TIs, ARPES allows for the most direct measurement of the dispersion of surface states, which can be used to determine the topological nature of the material. For two-dimensional TIs, the edge states have been studied in various transport experiments. As examples of the interesting physical properties of TIs, in Figure 2 we show some representative experimental data on (a) the conductance of the twodimensional QSH state in HgTe12 and (b) three-dimensional Bi2Te3 and Bi2Se3 surface states observed in ARPES.13,14 New physical effects, such as the quantum anomalous Hall effect (QAHE),15,16 topological magnetoelectric effect,17,18 and topological surface superconductivity,19 have been proposed for TIs, thus making TIs interesting candidate systems for
Claudia Felser, Max Planck Institute for Chemical Physics of Solids, Germany; [email protected] Xiao-Liang Qi, Stanford University, USA; xlqi
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