Tunneling Spectral And Impurity State In Several Systems

Defect, defined as breaking the translation or rotation symmetry of the host, plays an important role in studying the properties of condensed matter systems. It can help us better understand the ground state and excitations of the bulk materials. In this thesis, we investigate several different kinds of defect, including boundary, magnetic flux, potential impurity, structure step and magnetic impurity, located in different hosts covering iron-pnictide superconductors, topological insulators, band insulators and s-wave full-gap superconductors.In Chapter Ⅰ, we consider a tunneling junction connecting a normal metal and a multi-band superconductor. After deriving a generalized Landauer formula describ-ing the tunneling current, we first reproduce the main results of Blonder-Tinkham-Klapwijk theory, and then apply it to iron based superconductors. We find a novel quantum interference effect which can suppress the Andreev reflection. This effect can help us identify the gap symmetry of iron based superconductors.In Chapter Ⅱ, motivated by the observation of particle-hole asymmetry bound state inside the vortex core of iron based superconductors, we investigate this problem from different kinds of lattice models, including2-band,3-band and5-band models. We find the bound state asymmetry comes from the band edge effect in the normal state and is insensitive to the relative phase of gaps on different bands.In Chapter Ⅲ, we study the point impurity and terrace on the surface of a3D topological insulator. We attribute the oscillation of local density of state to the quasi-particle scattering between different momentums. As protected by spin-momentum coupling of surface Dirac states, we find no sign of back scattering. Our results are consistent with the scanning tunneling microscope experiment. In Chapter IV, we investigate the magnetic impurity inside a gapped system in-cluding a band insulator/semiconductor and an s-wave full-gap superconductor. For the semiconductor bath, only particle-hole asymmetric Anderson impurity induces a singlet-doublet quantum phase transition. For the s-wave superconductor, even in the particle-hole symmetric case, the singlet-doublet phase transition exists at zero tem-perature. Besides the zero temperature quantum phase transition, we find this singlet-doublet transition also occurs at finite temperature as decreasing the temperature.