| The negative band gap semiconductor materials---topological insulators, it is the most notable state of a kind of new material. Compared with ordinary insulators, the energy band structure of topological insulator is a kind of gapless, so there are edge or surface states which run throughout the band gap. However, the edge states or surface states of this inverted band gap semiconductor are fundamentally different from the local states that caused by ordinary impurities or defects. Then the topological insulators opened a new door for semiconductor Spintronics. The following are the main contents and results:(1)The electronic distribution of conventional semiconductor and the HgTe topological insulators of low dimensional structure; and also study the impact of the external magnetic on the HgTe topological quantum well, we found that the energy spectrum of the topological quantum well become no longer linear with respect to the vector k.(2)The properties of energy spectrum and electron distribution of two different shaped topological HgTe quantum dots, i.e., the square topological quantum dot and circular topological quantum dot, they are all have the property edge states, for the topological insulator quantum dots case M<0.(3)The spin property of circular topological quantum dot is investigated. When an external magnetic field is applied the circular topological quantum dot, the energy spectrum become no longer symmetric. The circular topological quantum dot doped with a single Mn2+ ions,then we find that the energy spectrum and the distribution of topological quantum dot both associated with the position of the magnetic Mn2+ ions in the quantum dots. When we dope a single polarized magnetic ion, the edge states with spin up is different from those with spin down because of the sp-d interaction. Nevertheless,we applied the external magnetic field along the Z direction,the energy spectrum of edge states will become unsymmetrical with respect to angular moment m. |
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