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In this work we have studied the tunneling processes that take place when an intense electric field is applied to a superconducting material, using a many body approach. In particular we were interested in the energy spectrum of emitted electron. We explained previous work on the subject, which considered only processes where a single electron tunneling happened at a given time. In this framework the energy gap of the superconductor appears in the spectrum and no tunnelings take place for these energies.
Our work focused instead on the possibility of a double tunneling, where two electrons coming from the same Cooper pair are emitted at the same time. This is an Andreev process, and could happen for energies inside the superconductor's gap, contrary to the single electron case. In this energy range we derived an analytic formula for the current density spectrum of Andreev processes.
Since these processes are of a higher order using perturbation theory, they would normally be very dicult to see. However inside the gap they are the only non-zero contribution to the current. The final result we found is still impossible to give an experimental confirmation, mainly because there are some unexplained distortions in the single particle spectrum which made impossible to see the gap in previous experiments.