The Quantum Hall Effect with Wilczek's charged magnetic flux tubes instead of electrons

TL;DR

This paper proposes a method to realize Wilczek's anyons using a high-permeability material to create flux tubes in a 2D electron system exhibiting the IQHE, leading to detectable resistivity shifts.

Contribution

It introduces a novel scheme to generate charged flux tubes and realize anyons in a quantum Hall system using high-$_r$ materials with fast response times.

Findings

The scheme can produce Wilczek's anyons in a 2D electron system.

A measurable shift in IQHE resistivity signals the presence of anyons.

High-$_r$ metamaterials are key to this realization.

Abstract

Composites formed from charged particles and magnetic flux tubes, proposed by Wilczek, are one model for anyons - particles obeying fractional statistics. Here we propose a scheme for realizing charged flux tubes, in which a charged object with an intrinsic magnetic dipole moment is placed between two semi-infinite blocks of a high permeability ($\mu_r$) material, and the images of the magnetic moment create an effective flux tube. We show that the scheme can lead to a realization of Wilczek's anyons, when a two-dimensional electron system, which exhibits the integer quantum Hall effect (IQHE), is sandwiched between two blocks of the high-$\mu_r$ material with a temporally fast response (in the cyclotron and Larmor frequency range). The signature of Wilczek's anyons is a slight shift of the resistivity at the plateau of the IQHE. Thus, the quest for high-$\mu_r$ materials at high frequencies, which is underway in the field of metamaterials, and the quest for anyons, are here found to be on the same avenue.