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

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.