Possibility for a novel type of sensors for detecting nanosized substances (e.g., macromolecules or molecule clusters) through their effects on electron tunneling in a double nanoscale semiconductor heterostructure is discussed. We studied spectral distributions of localized/delocalized states of a single electron in a double quantum well (DQW) with relation to slight asymmetry perturbations. The asymmetry was modeled by modification of the dot shape and the confinement potential. Electron energy uncertainty is restricted by the differences between energy levels within the spectra of separated QWs. Hence, we established a direct relationship between the uncertainty of electron localization and the energy uncertainty. We have shown in various instances that a small violation of symmetry drastically affects the electron localization. These phenomena can be utilized to devise new sensing functionalities. The charge transport in such sensors is highly sensitive to minuscule symmetry violation caused by the detected substance. The detection of the electron localization constitutes the sensor signal.

A new generation of nanosensors is underway and is expected to revolutionize modern engineering fields, including bioengineering and drug delivery systems in nanomedicine, to name a few. Semiconductor heterostructures, such as quantum dots and rings, are of high interest for the development of these nanosensors, as well as many other predicted nanodevices. Of particular importance is the electron tunneling that occurs between the nanosized elements of such devices. Double quantum systems facilitate the study of tunneling related to barrier penetration effects in double well potentials [

In the present work we study the spectral distribution of electron localized/delocalized states and tunneling in DQWs. The average coordinate is used to characterize the localization of a single electron. We discuss the case of identical QWs constituting a DQW, as an example, when the uncertainty principle is manifested. Uncertainty of electron localization occurs when the difference of electron energies in the left and right QW is very small; that is the case of almost identical QWs. The symmetry violation caused by differences in the geometry and/or the confinement potentials in left and right QWs is thoroughly discussed.

We consider quantum dots composed of InGaAs on a GaAs substrate. The fabrication of such kind of quantum dots is reported in [

Here

Single electron spectrum of a two-level system is defined as a set of quasidoublets [

Band gap model for one-dimensional DQW.

In (

To evaluate the electron localization, we analyze the single electron average coordinate

Relation between the parameter

According to relation (

Due to the square in the denominator, small variations of

The experimentally demonstrated circular disc shaped InAs/GaAs quantum dots constitute double quantum wells. We consider in this section identical quantum wells, with equal radii

The electron average coordinate

Effects of the interdot distance,

To evaluate the accuracy of the calculations we applied different meshes. Figure

Spectral distributions for the average coordinate

Visualization of the localized-delocalized states dynamics in the InAs/GaAs DQW is given in Figure

Average coordinate

Additionally, as can be seen in (

Let us consider two circular QWs that are nonidentical. The asymmetry parameter for the DQW is defined as

Average coordinate,

Comparing with the previously discussed identical DQWs, for asymmetric DQW, the interdot distance that causes the quantum states to become delocalized, over the entire spectrum, is smaller. For example, when

It has been previously found [

Typical picture for the spectral distribution of average coordinate

(a) Spectral distribution of

The matrix element

The symmetry breaking in DQW can be also made by variations of the confinement strength in one of the QWs. In Figure

Single electron average coordinate

One more illustration of symmetry breaking effect is given in Figure _{2}). The average coordinate

(a) Circle shaped DQW exhibiting an asymmetry generated by truncating the right quantum well (QW_{2}). (b) Electron average position

An additional illustration of the symmetry breaking effect is presented in Figures

(a) Energy differences

Average coordinate

The violation of DQW shape symmetry largely effects the spectral distribution of localized/delocalized states by varying the energy level splitting, manifested by a large energy difference _{2}, as is shown in Figure

(a) Semicircle shaped DQW, where the asymmetry is generated by a rectangular defect in the right QW. The defect height,

It appears from data in Figure

We studied the spectral distribution of localized/delocalized states in DQW. The electron localization in DQW appeared extremely sensitive to small violations of symmetry in DQWs due to relation (

The observed electron behavior in double quantum structures can be interpreted in terms of the uncertainty principle. We have shown that the spectral distribution of the electron average coordinate

We demonstrated that the DQW is a quantum system suitable for sensing tiny substances adsorbed on one of the quantum dots constituting the DQW or by a defect in one of the dots. The protuberance volume capable of breaking the symmetry, changing the quantum states of the DQW, and provoking tunneling was estimated to contain one to several thousand atoms, which is in the range of the size of polymer macromolecules and biomolecules.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by NSF (HRD-1345219) and MSRDC consortium (Award 001 W911SR-14-2-0001-0002).

_{2}and 2

_{2}: fracturing of a flux line lattice