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

TL;DR

This paper derives exact solutions for relativistic electron scattering through a double barrier potential, revealing multiple transmission resonance regions including sub-barrier resonances within Klein zones.

Contribution

It provides the first exact relativistic solutions for a double barrier with specific potential configurations, uncovering new sub-barrier resonance phenomena.

Findings

Identification of three distinct transmission resonance regions

Discovery of broader sub-barrier resonances within Klein zones

Extension of conventional double barrier resonance understanding

Abstract

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.