Renormalization of the expression for the superconducting tunnelling currents

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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.

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