Energy Spectrum And Bound States Of Electron On The Surface Of Topological Insulator

The peculiar edge states of the surface on topological insulator leads to that the backscattering of the electrons can not occur on the surface and the electrons can move on the surface without the loss of the energy, which provides the advantageous conditions for solving the cooling problems of the CMOS chip when it gets smaller and smaller. The operation speed of electron devices based on topological insulator is faster than traditional semiconductor devices and save energy. Topological insulator has attracted an enormous of attention in the fields of condensed matter physics, material science and information technology. However, since Dirac electrons obey the massless Dirac equation on the surface of a topological insulator, it is difficult to restrict electron by using electrostatic potential. To explore the way of restricting and controlling Dirac electrons is very important in actualizing quantum devices using topological insulator. The thesis studies the bound states and spectrum of Dirac electrons in circular and annular quantum dot and discusses the restriction of Dirac electrons on an inhomogeneous magnetic field.The following are the main contents and results:(l)The inhomogeneous magnetic field is formed on the surface of topological insulator by the adjacent effect of magnetic film, which circular magnetic potential quantum dot is constructed. The bound states and spectrum of Dirac electrons in circular quantum dot are investigated. The inhomogeneous magnetic field eliminates partly the degeneracy of Landau level and the condition of forming bound states is given in a circular quantum dot. The level of the circular quantum dot lifts with the decrease of the radius of the circular quantum dot, and when the radius approach zero Dirac electron occupies Landau level. With the radius increasing the level of the bound states debases and when the radius increases reaches at certain value the state (n, m) and (n,-m) degenerate for the large radius. Moreover, we study the probability distribution and persistent current of Dirac electrons in quantum dot.(2) The energy spectrum and bound states of Dirac electron on the surface of topological insulator under the restriction of magnetic potential are investigated. We discuss the influence of the radius of quantum dot on the energy spectrum and give the condition of the form of bound states in a circular quantum dot by the restriction of magnetic potential barrier. When the radius of the circular quantum dot approach zero Dirac electron occupies Landau level and the state (n, m) and (n,-m) degenerate for the large radius.For the annular quantum dot, the bound states emerge only when the ratio of the inner and outer radius of the ring is less than a critical value. When the ratio is larger than the critical value the energy level restore Landau level. The bound levels may be modulated by changing the magnetic field and the radius of the dot or ring, which is useful in designing topologically-protected quantum devices.