Breaking time reversal symmetry in topological insulators
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Introduction Topological insulators (TIs), predicted and observed, display helical metallic surface states (SSs) obeying a Dirac-type linear energy-momentum dispersion relation that are protected by time reversal symmetry (TRS).1–6 Upon a time reversal operation, which leads the system to evolve backward in time, the electron wave vector k and the spin will flip the sign. The helical surface states of a topological insulator are invariant under such operation since the opposite spin channels are locked to the opposite momenta. In the presence of magnetic field or magnetic impurities, however, this invariant or symmetry will be broken. Although the TI is an ordered phase not relying on broken symmetry, the symmetry broken states created in a TI have been predicted to carry many novel quantum phenomena1,2 (e.g., the quantum anomalous Hall effect [QAHE],7–9 topological magnetoelectric effect,7,10 as well as image magnetic monopole11). The unique properties exhibited by these systems open up avenues for both fundamental physics research and new materials displaying exotic phenomena aimed at technological applications. The spontaneously broken time reversal symmetry states can be experimentally introduced into a material by ferromagnetic ordering. This may usually be achieved by two methods that are described in the following paragraphs: (1) conventionally by doping with some magnetic element and (2) by ferromagnetic proximity coupling. In both cases, it is expected
that an exchange gap opens in the Dirac SS.7 Although this seems straightforward, the major difficulty remains in reducing the bulk conduction, particularly in thin films, and thus it is a daunting task for any TI material system. This difficulty hinders observations of the predicted properties of TIs with broken TRS. Similar to conventional diluted magnetic semiconductors (DMSs),12–14 impurity doping using transition metal (TM) elements (e.g., Cr, V, Mn) is a convenient approach to induce long-range ferromagnetic order in TIs (Figure 1a). Many recent experiments, from angle-resolved photoemission spectroscopy (ARPES) to electrical transport measurements, have been devoted to the study of magnetically doped TIs of the Bi2Se3 family, including Bi2Se3, Bi2Te3, and Sb2Te3.15–23 In magnetically doped Bi2Te3 and Sb2Te3, both transport and magnetization measurements have shown clear long-range ferromagnetic order in several cases,20–23 which resulted in the observation of QAHE (the quantum Hall effect [QHE] without an external magnetic field).23 The Zeeman gap opening, which is the splitting of the energies between the spinup and spin-down electron states under the influence of an external or effective internal magnetic field at the SS Dirac cone, however, has not been resolved by ARPES or scanning tunneling spectroscopy (STS) in ferromagnetic TIs, possibly due to their low Curie temperature (TC) and small gap size. On the other hand, for magnetically doped Bi2Se3, the SS Zeeman
Cui-Zu Chang, Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology, USA; cz
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