Theory of Tunneling Spectroscopy of Multi-Band Superconductors

We present the derivation of boundary conditions on a wave function at the normal metal/superconductor (N/S) interface by extending the tight-binding approach developed for semiconducting heterostructures [Phys. Rev. 27 (1983) 3519]. Based on these boundary conditions, we formulate a quantitative theory for tunneling spectroscopy in N/S junctions, where a superconductor is characterized by complex non-parabolic energy spectrum beyond effective mass approximation. As an application to single-band unconventional superconductors, we re-derive the known conductance formula [Phys. Rev. Lett. 74 (1995) 3451] with generalized definition of a normal-state conductance. We further apply the model to junctions between normal metals (N) and multi-band iron-based superconductors (FeBS). Our calculations show that tunneling studies of (100) oriented N/FeBS junctions allow to distinguish between the s ± and the s ++ order parameter symmetry in FeBS. In low transparent N/FeBS junctions with the s +− symmetry in FeBS, finite energy subgap Andreev bound states are formed due to sign change of pair potential between different Fermi surface pockets. Another fingerprint of the s +− symmetry in FeBS is suppressed Andreev conductance in high transparent (100) N/FeBS junctions compared to the case of the s ++ symmetry. Our results may serve as a basis for quantitative tunneling spectroscopy of FeBS