One crucial and important aspect to account for the nature of the quantum wires is the understanding of the effects associated to many-body interactions between confined electrons. The inclusion of such many-body forces in any theoretical framework is a difficult and computationally demanding task. Then one has to make use of coarse-grained descriptions that allow one to incorporate the contribution of all the electrons. In a simple physical picture, the interaction between two electrons can be considered screened due to the presence of the other ones. If the latter are homogeneously distributed inside the wire, the interaction between the former can then be assumed of the Yukawa form. In this contribution, we report on the lower energy states of $n$-doped GaAs circular-quantum wires with two electrons in the conduction band interacting through a repulsive Yukawa potential. By varying the length and the electronic density of the wire, quite different trends in the electronic distribution are observed. By changing the material parameters to InSb and InAs nanowires, we found that our results are consistent with available experimental data that have reported the formation of Wigner crystals.

Vertically aligned arrays are a frequent outcome in the nanowires synthesis by self-assembly techniques or in its subsequent processing. When these nanowires are close enough, quantum electron tunneling is expected between them. Then, because extended or localized electronic states can be established in the wires by tuning its electron density, the tunneling configuration between adjacent wires could be conveniently adjusted by an external gate. In this contribution, by considering the collective nature of electrons using a Yukawa-like effective potential, we explore the electron interaction between closely spaced, parallel nanowires while varying the electron density and geometrical parameters. We find that, at a low-density Wigner crystal regime, the tunneling can take place between adjacent localized states along and transversal to the wires axis, which in turn allows to create two- and three-dimensional electronic distributions with valuable potential applications.