Possible $s^{\pm}$-wave pairing evidenced by midgap surface bound states in Fe-pnictide superconductors

A phenomenological theory of tunneling spectroscopy for Fe-pnictide superconductors is developed by taking into consideration of asymmetric interface scattering between particle and holes. It is shown that in consistent with anti-phase $s^{\pm}$-wave pairing, appreciable zero-energy surface bound states exist on the [100] surface of Fe-pnictide superconductors. However, in contrast to the [110] bound states in $d$-wave cuprate superconductors, these bound states arise as a result of non-conservation of momentum perpendicular to the interface for tunneling electrons and the $s^{\pm}$ pairing, and hence they can only exist in a small window ($\sim \pm 6^{\circ}$) in the orientation of edges near [100] direction. Our results explain why zero-bias conductance peak is often observed in tunneling spectroscopy and when it disappears, two coherent peaks show up. These results provide unambiguous signals to test the possible $s^{\pm}$-wave pairing in Fe-pnictide superconductors.