2-Dimensional Electron Gas in a Linearly Varying Magnetic Field. ``Quantisation'' of the Electron and Current Density

TL;DR

This paper introduces new analytical methods to study electron and current density distributions in a 2D electron gas subjected to a linearly varying magnetic field, revealing complex quantization effects and spin contributions.

Contribution

It develops novel analytical techniques for calculating dispersion curves and spatial distributions in non-uniform magnetic fields, including spin effects.

Findings

Electron and current densities show rich quantization-related structures.

Spin contributes directly to the current density, indicating potential for spin-polarized currents.

Results provide insights into properties of linearly varying magnetic fields.

Abstract

We have developed new methods to calculate dispersion curves (analytically in the simpler cases) from which we are able to derive the spatial distribution of electron and current densities. We investigate the case where the magnetic field varies linearly with position and the results provide useful insights into the properties of this and other field distributions. We consider spin as well as a confining electrostatic potential. We show that the electron and the current density exhibit a very rich structure related to the quantisation of the energy. Moreover there is a direct contribution to the current density due to the spin which could be of interest in relation to spin polarised current.