Relativistic Double Barrier Problem with Three Sub-Barrier Transmission Resonance Regions

We obtain exact scattering solutions of the Dirac equation in 1+1 dimensions for a double square barrier vector potential. The potential floor between the two barriers is higher than 2mc^2 whereas the top of the barriers is at least 2mc^2 above the floor. The relativistic version of the conventional double barrier transmission resonance is obtained for energies within + or - mc^2 from the height of the barriers. However, we also find two more (sub-barrier) transmission resonance regions below the conventional one. Both are located within the two Klein energy zones and characterized by resonances that are broader than the conventional ones.