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

Abstract

The fractional quantum Hall effect (FQHE) has been considered as a puzzling quantum manybody phenomenon that has yet to be fully explained. The experimentally measured Hall resistivity curve must be clarified based on quasiparticle energy gaps, and therefore, revealing the relation between plateau widths and energy gaps is key to fully understand the electron transport that causes the FQHE. Here, we report that a quasiparticle of spin unity comprising an electron and its image replacing the confining potential of an incompressible strip appropriately describes the dynamics of electrons moving through the narrow strip under high magnetic field, and also that correlated quasiparticles formed by many-body interaction have higher integral spins and play a crucial role. The Zeeman effect for individual quasiparticles of spin unity splits a degenerated Landau level into three sublevels, which produces plateaus of filling factor with denominator three, and each sublevel splits again into five sublevels due to two correlated quasiparticles with total spin two, which produces plateaus of filling factors with denominator five. This level splitting continues with higher-order quasiparticle correlation. With such a scheme, we explicitly show that plateau widths and energy gaps are connected via the degrees of multi-particle correlation and reproduce experimental Hall resistivity and energy gaps, Only the lowest Landau level is studied, where plateaus of even-denominator filling factors do not appear.