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Impurity-potential-induced gap at the Dirac point of topological insulators with in-plane magnetization

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 Added by Md Islam
 Publication date 2019
  fields Physics
and research's language is English




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The quantum anomalous Hall effect (QAHE), characterized by dissipationless quantized edge transport, relies crucially on a non-trivial topology of the electronic bulk bandstructure and a robust ferromagnetic order that breaks time-reversal symmetry. Magnetically-doped topological insulators (TIs) satisfy both these criteria, and are the most promising quantum materials for realizing the QAHE. Because the spin of the surface electrons aligns along the direction of magnetic-impurity exchange field, only magnetic TIs with an out-of-plane magnetization are thought to open a gap at the Dirac point (DP) of the surface states, resulting in the QAHE. Using a continuum model supported by atomistic tight-binding and first-principles calculations of transition-metal doped Bi$_2$Se$_3$, we show that a surface-impurity potential generates an additional effective magnetic field which spin-polarizes the surface electrons along the direction perpendicular to the surface. The predicted gap-opening mechanism results from the interplay of this additional field and the in-plane magnetization that shifts the position of the DP away from the $Gamma$ point. This effect is similar to the one originating from the hexagonal warping correction of the bandstructure but is one order of magnitude stronger. Our calculations show that in a doped TI with in-plane magnetization the impurity-potential-induced gap at the DP is comparable to the one opened by an out-of-plane magnetization.



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Topological insulators are novel macroscopic quantum-mechanical phase of matter, which hold promise for realizing some of the most exotic particles in physics as well as application towards spintronics and quantum computation. In all the known topological insulators, strong spin-orbit coupling is critical for the generation of the protected massless surface states. Consequently, a complete description of the Dirac state should include both the spin and orbital (spatial) parts of the wavefunction. For the family of materials with a single Dirac cone, theories and experiments agree qualitatively, showing the topological state has a chiral spin texture that changes handedness across the Dirac point (DP), but they differ quantitatively on how the spin is polarized. Limited existing theoretical ideas predict chiral local orbital angular momentum on the two sides of the DP. However, there have been neither direct measurements nor calculations identifying the global symmetry of the spatial wavefunction. Here we present the first results from angle-resolved photoemission experiment and first-principles calculation that both show, counter to current predictions, the in-plane orbital wavefunctions for the surface states of Bi2Se3 are asymmetric relative to the DP, switching from being tangential to the k-space constant energy surfaces above DP, to being radial to them below the DP. Because the orbital texture switch occurs exactly at the DP this effect should be intrinsic to the topological physics, constituting an essential yet missing aspect in the description of the topological Dirac state. Our results also indicate that the spin texture may be more complex than previously reported, helping to reconcile earlier conflicting spin resolved measurements.
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