Duality in Multi-layered Quantum Hall Systems

TL;DR

This paper explores the duality properties in multi-layered quantum Hall systems, providing new theoretical tools to analyze fractional charges, statistics, and filling factors, and predicting novel quantum Hall states.

Contribution

It introduces a generalized duality framework for multi-layered quantum Hall systems and proposes a wavefunction for bilayered samples, predicting a new FQHE state at ν=5/7.

Findings

Proposes a many-quasi-hole wavefunction for bilayer systems

Predicts a ν=5/7 FQHE in triple-layered samples

Discusses the potential for 3D FQHE and anyonic superconductivity

Abstract

The braid group dynamics captures the fractional quantum Hall effect (FQHE) as a manifestation of puncture phase. When the dynamics is generalized for particles on a multi-sheeted surface, we obtain new tools which determine the fractional charges, the quantum statistics, and the filling factors of the multi-layered FQHE. A many-quasi-hole wavefunction is proposed for the bilayered samples. We also predict a $\nu = 5/7$ FQHE for triple-layered samples. The viability of {\em 3-dimensional} FQHE and the application of the concept of generalized duality to anyonic superconductivity are discussed.