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

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