Fractional charge in quantum Hall effect

TL;DR

This paper reviews the concept of fractional charge in the quantum Hall effect, discussing historical theoretical proposals and presenting a new approach using orbital angular momentum and spin consistent with experimental data.

Contribution

It introduces a novel method to define fractional charge using orbital angular momentum and spin, aligning theory with quantum Hall effect observations.

Findings

Fractional charge can be derived from orbital angular momentum and spin.

The approach aligns with experimental quantum Hall data.

Historical theories are compared and contextualized.

Abstract

In 1976 Jackiw and Rebbi found 1/2 of a fermion number by using Dirac equation in 1+1 dimensions. Schrieffer in several proposals made an effort to suggest that there is a fractional charge. The calculations of Peierls distortion, Berry's phase and classical action were presented to accomodate the fractional charge in non-relativistic theory. Laughlin used the antisymmetry to define the charge density per unit area in a two dimensional system. In order to elliminate the area, Laughlin introduced the incompressibility which fixed the area so that the odd number, which determines the antisymmetry of the electron wave function, gave the charge. We have used the orbital angular momentum and the spin to define the charge, in full agreement with the quantum Hall effect data.