Quasiparticle states in superconducting superlattices
  The energy bands and the global density of states are computed for superconductor / normal-metal superlattices in the clean limit. Dispersion relations are derived for the general case of insulating interfaces, including the mismatch of Fermi velocities and effective band masses. We focus on the influence of finite interface transparency and compare our results with those for transparent superlattices and trilayers. Analogously to the rapid variation on the atomic scale of the energy dispersion with layer thicknesses in transparent superlattices, we find strong oscillations of the almost flat energy bands (transmission resonances) in the case of finite transparency. In small-period transparent superlattices the BCS coherence peak disappears and a similar subgap peak is formed due to the Andreev process. With decreasing interface transparency the characteristic double peak structure in the global density of states develops towards a gapless BCS-like result in the tunnel limit. This effect can be used as a reliable STM probe for interface transparency. 
Mihajlo Vanevic and Zoran Radovic