Klein paradox with spin-resolved electrons and positrons

Using numerical solutions to relativistic quantum field theory with space-time resolution, we illustrate how an incoming electron wave packet with a definite spin scatters off a supercritical potential step. We show that the production rate is reduced of only those electrons that have the same spin as the incoming electron is reduced. This spin-resolved result further clarifies the importance of the Pauli-exclusion principle for the Klein paradox.