Theory of Tunneling Spectroscopy in LaFeAsO$_{1-x}$F$_{x}$

Recent discovery of superconductivity in the iron based LaFeAsO$_{1-x}$F$_{x}$ with Tc = 26K has stimulated great interests as a new class of non-cuprate compound. We calculate the surface density of state of LaFeAsO$_{1-x}$F$_{x}$ superconductor. The gap function is obtained microscopically by solving the Eliashberg equation in a 5-band Hubbard model with the random phase approximation (RPA). Green's function of the surface state is obtained by inserting infinite potential barriers using Matsumoto and Shiba method. Although the gap function has a sign change between Fermi surfaces, we cannot find mid gap Andreev bound state in [100] and [110]-oriented interface.