Origin of resonant tunneling through single-point barriers

Highlights: • The conditions for resonant tunneling through single-point barriers are derived. • This effect is proved to occur in a barrier-well structure as it squeezes to one point. • The special requirement on the reflection coefficients is shown to provide the resonance conditions. The physical interpretation of the appearance of resonant transmission through single-point barriers is discussed on the basis of a double-layer heterostructure in the squeezing limit as both the thickness of the layers and the distance between them tend to zero simultaneously. In this limit, the electron transmission through a barrier-well structure is derived to be non-zero at certain discrete values of the system parameters forming the so-called resonance set, while beyond this set, the structure behaves as a perfectly reflecting wall. The origin of this phenomenon is shown to result from the reflection coefficients at the interfaces in the inter-layer space. The transmission amplitude is computed as a set function defined on the trihedral angle surface in a three-dimensional parameter space.