Renormalization of the expression for the superconducting tunnelling currents

Abstract

The singularities of the expressions for the superconducting tunnelling currents are shown to be caused by the fact that they are derived via a perturbation calculation of finite order. A general formula for the current density valid for large tunnelling matrix elements and exterior electromagnetic fields is derived. Then it becomes possible to obtain a broadened quasiparticle current step and a finite Riedel peak. In addition, a renormalized second order quasiparticle current is shown to be finite for every DC voltage. The method employed is to sum the corresponding types of diagrams to infinite order.