The Reflection Of Interface State Between Two Topological Insulators And The Shot Noise In The Semidirac-Point Symstem

According to their electric conductivity, solid-state materials can be divided into conductors, insulators and semiconductors. With the further study on solids, new states of matter with topological character are found. In this thesis, we study the quantum transport on the surface of three-dimensional topological insulators and in semi-Dirac systems. Firstly, we revisit the result concluded from Phys. Rev. Lett.107,166805(2011): the interface between two kinds of topological insulators with opposite Fermi velocities, electrons at normal incidence will neither be reflected nor be transmitted. We find that this striking conclusion is questionable due to the incompleteness of the adopted linear-in-momentum Hamiltonian. Then the Hamiltonian including the band-warping effect and the modification of Fermi velocities is used to describe the scattering problem of this heterostructure. The calculation based on this Hamiltonian reveals that for this topological heterostructure, perfect transmission always happens for electrons at normal incidence. This conclusion agrees with the symmetry analysis. In the second part of this thesis, we study the shot noise of semi-Dirac systems. Along the linear-dispersion direction, the Fano factor at the semi-Dirac point has a universal value F=0.179that has not been reported so far. The conductivity at the semi-Dirac point, however, has not a minimum. This differs greatly from the results for graphene. At the Dirac point, graphene samples have a minimum conductivity and a universal Fano factor F=1/3. Along the parabolic dispersion direction the shot noise at semi-Dirac point is close to0.958. We explain these results by means of the transmission spectrum. Our findings indicate that the measurement on shot noise may be utilized to discern the type of band-touching points.