Interaction Potential between a Uniformly Charged Square Nanoplate and Coplanar Nanowire

Abstract

We study a structure consisting of two electrostatically interacting objects, a uniformly charged square nanoplate and a uniformly charged nanowire. A straightforward motivation behind this work is to introduce a model that allows a classical description of a finite two-dimensional quantum Hall system of few electrons when the Landau gauge is imposed. In this scenario, the uniformly charged square nanoplate would stand for the neutralizing background of the system while a uniformly charged nanowire would represent the resulting quantum striped state of the electrons. A second important feature of this model is that it also applies to hybrid charged nanoplate-nanowire systems in which the dominant interaction has electrostatic origin. An exact analytical expression for the electrostatic interaction potential between the uniformly charged square nanoplate and coplanar nanowire is obtained by using a special mathematical method adept for this geometry. It is found that the resulting interaction potential is finite, monotonic and slowly-varying for all locations of the nanowire inside the nanoplate.

A Charged Particle with Anisotropic Mass in a Perpendicular Magnetic Field–Landau Gauge

“…is known as the magnetic length. By looking at the expression obtained in Equation ( 19), one concludes that the normalized eigenfunctions for a charged particle studied in a Landau gauge look like stripes [33]. It is straightforward to note that the probability density for such eigenfunctions, |Ψ n k y (X, y)| 2 , depends only on the variable X (thus, x), but not y.…”