Origin of resonant tunneling through single-point barriers

Abstract

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.

Band spectra of periodic hybrid $δ$-$δ^\prime$ structures

“…After the seminal paper by Kurasov where contact potentials are characterised by certain self adjoint extensions of the one-dimensional kinetic operator K = −d 2 /dx 2 [21], several attempts have been made to explain the physical meaning of the contact potentials that emerge from these extensions [22,23]. More recently there have been papers where, contact potentials have been used to study the effects of resonant tunneling [24,25], to study their properties under the effect of external fields [26], and their applications in the study of metamaterials [27]. In addition the effects of several contact potential barriers have been studied in [28,29,30,31,32,33] and extensions to arbitrary dimension have been considered in [34] generalising the approach by Jackiw in [15].…”

Conditions for realizing one-point interactions from a multi-layer structure model

“…The most simple example of regularizing the δ -potential is the sequence of piecewise constant functions, which from the physical point of view can be related to planar heterostructures. In particular, for the double-layer case, using a three-scale parametrization of the layer parameters such as their strengths, thickness and the distance between the layers, a whole family of one-point interactions has been constructed, where the scattering data [13,33,34] as well as the existence of a bound state [35,36] have been examined. In general, here it is not required that a piecewise constant potential must have a well-defined limit (for instance, in the sense of distributions) as the thickness of layers and the distance between them shrink to zero.…”