Dipoles and fractional quantum Hall masses

TL;DR

This paper presents a microscopic formalism for fractional quantum Hall states at various filling factors, deriving quasiparticle charges, wave functions, and effective masses that align with experimental observations.

Contribution

It introduces a novel microscopic approach that accurately predicts quasiparticle properties and wave functions, extending understanding of fractional quantum Hall effects beyond previous models.

Findings

Wave functions match Jain's predictions regardless of interaction potential.

Computed effective masses agree with experimental data at ν=1/2 and 1/4.

Identifies a universal bound state formation from attractive charges in Landau levels.

Abstract

We develop a microscopic formalism to study the fractional quantum Hall plateaus at filling factors $\nu $ away from $1/2\beta$ $\beta$ an integer. The theory is in terms of quasiparticles which carry a charge $e^{\ast}$ equal to $1-2\beta\nu $ times the charge of the electron. The wave functions obtained following our approach are shown to coincide precisely with the form predicted by Jain and this holds independently of the interaction potential.\ Microscopically this rigidity originates from the fact that two different charges interacting attractively in their lowest Landau levels form a bound state with a universal wave function. From the expressions of the gaps we compute an effective mass which agrees well with the experiments carried at $\nu=1/2$ and 1/4.