Determination of Plateau Widths and Energy Gaps in the Fractional Quantum Hall Effect by Multi-Particle Correlations

TL;DR

This paper investigates how multi-particle correlations influence the widths of plateaus and energy gaps in the fractional quantum Hall effect, providing a theoretical model that reproduces experimental observations.

Contribution

It introduces a new theoretical framework linking multi-particle correlations to the fine structure of the Landau level and fractional quantum Hall plateaus.

Findings

Reproduces experimental Hall resistivity data

Links quasiparticle spin states to energy gap formation

Explains fine structure splitting via many-body interactions

Abstract

Determining plateau widths and energy gaps is the remaining task to fully understand the electron transport that gives the fractional quantum Hall effect at the lowest Landau level (LLL). We report that this determination is given by the degree of multi-particle correlations that governs the split distance of the fine structure of the LLL.We show that an electron flowing through an incompressible strip formed in a Hall bar behaves as a quasiparticle comprising the electron and its image, which replaces the confining potential of the incompressible strip. This quasiparticle is a composite boson of spin unity. Correlated quasiparticles having higher integral spins are induced by many-body interactions. The Zeeman effect for these integral spins of the quasiparticles yields fine splits in the LLL, which is responsible for the plateaus in Hall resistivity at fractional fillings. With such a scheme, we explicitly reproduce experimental Hall resistivity and energy gaps.