Exactly pairing two-dimensional charged particles using a magnetic field

TL;DR

This paper shows that two-dimensional charged particles can be exactly paired using a magnetic field only at specific quantized intensities, revealing a shell structure and explaining quantum Hall effect phenomena.

Contribution

It introduces a precise condition for pairing 2D charged particles with magnetic fields and links theoretical predictions to experimental quantum Hall data.

Findings

Pairing occurs only at specific quantized magnetic intensities.

Degeneracy in center-of-mass Landau levels leads to shell structure.

Theoretical results align with quantum Hall plateau data.

Abstract

It is demonstrated that a uniform magnetic field can exactly pair the two-dimensional (2D) charged particles only for some quantized magnetic intensity values. For the particle-pair consisting of two like charges the Landau level of the center-of-mass motion is multiple degenerate that implies the shell structure. However, any particle-pair has only two non-degenerate relative levels, which are associated with the diamagnetic and paramagnetic states respectively. There exist a upper critical magnetic strength and a lower critical magnetic length across which two like charges cannot be paired. The theoretical results agree with the experimental data on the sites and widths of the integral and fractional quantum Hall plateaus in a CaAs-Al$_x$Ga$_{1-x}$As heterojunction, that gives a new explanation for the quantum Hall effect.