Relativistic theory of transport in a normal/superconducting microconstriction

In this paper we develop a relativistic model of a normal–superconductor junction based on the generalized semiconductor model together with the Dirac–Bogoliubov–de Gennes equations to describe the reflection and transmission of particles at an N–S boundary with a barrier potential. The theory is illustrated with a calculation of the I–V curves, the differential conductance and the excess current. As expected, we observe that relativistic effects are very small in

superconducting junctions, but their effect is to increase the effective strength of the barrier.