Hari P. Paudel, Michael N. Leuenberger
3D topological insulators (TIs) are materials with topologically protected interface/surface states of massless Weyl fermions. This protection is manifested by the suppression of the backscattering caused by nonmagnetic impurities and edges on the surfaces and by the robustness against any type of surface modifications. Consequently, 3D TI nanostructures are very interesting because of their large surface-to-volume ratio. The topological surface states in nanostructures exhibit a phase coherence length of several hundred nanometers. Experiments on both the physical and chemical synthesis of TI nanostructures were performed recently to understand their transport properties at the nanoscale. Here we show the model of a quantum dot (QD) consisting of a spherical core-bulk heterostructure made of 3D TI materials, such as PbTe/Pb$_{0.31}$Sn$_{0.69}$Te, with bound massless and helical Weyl states existing at the interface and being confined in all three dimensions. The number of bound states can be controlled by tuning the size of the QD and the magnitude of the core and bulk energy gaps, which determine the confining potential. We demonstrate that such bound Weyl states can be realized for QD sizes of few nanometers. We identify the spin locking and the Kramers pairs, both hallmarks of 3D TIs. In contrast to topologically trivial semiconductor QDs, the confined massless Weyl states in 3D TI QDs are localized at the interface of the QD and exhibit a mirror symmetry in the energy spectrum. Because of the possibility to generate spin currents, the 3D TI QD opens up avenues to develop nanostructures for spintronics devices.
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http://arxiv.org/abs/1212.6772
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