Two-dimensional finite quantum Hall clusters of electrons with anisotropic features

Abstract

Low-dimensional nano and two-dimensional materials are of great interest to many disciplines and may have a lot of applications in fields such as electronics, optoelectronics, and photonics. One can create quantum Hall phases by applying a strong magnetic field perpendicular to a two-dimensional electron system. One characterizes the nature of the system by looking at magneto-transport data. There have been a few quantum phases seen in past experiments on GaAs/AlGaAs heterostructures that manifest anisotropic magnetoresistance, typically, in high Landau levels. In this work, we model the source of anisotropy as originating from an internal anisotropic interaction between electrons. We use this framework to study the possible anisotropic behavior of finite clusters of electrons at filling factor 1/6 of the lowest Landau level.

Interaction Potential between a Uniformly Charged Square Nanoplate and Coplanar Nanowire

“…In this picture, the uniformly charged square nanoplate would represent the neutralizing jellium background of the system while the uniformly charged nanowire would represent the striped state of the electron that emerges in a Landau gauge. These are the conditions where quantum Hall behavior is encountered and a quantum treatment is required [36][37][38][39][40][41]. Nonetheless, it is logical to argue that an classical model of the nature considered in this work may work reasonably well as long as we are dealing with small systems of electrons that obviously are confined to a small 2D domain with dimensions in the nanoscale (though with L markedly larger than l B which represents the width of the striped state).…”

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

“…In primed variables, this anisotropic Coulomb interaction potential (for γ ̸ = 1) breaks the usual assumption of isotropic pair interaction potentials. It is expected that an anisotropic interaction potential of this nature can steer us towards novel conceptual frameworks [37]. The idea is to deal with the rarely tackled, but considerably more difficult, problem of understanding how anisotropic order arises in a quantum system in which the constituent particles interact with an anisotropic interaction potential.…”