Quantum Hall Spherical Systems: the Filling Fraction

TL;DR

This paper explores the filling fractions in spherical quantum Hall systems within the composite fermion hierarchy, revealing fractional quantum Hall structures and confirming particle-hole symmetry relations for large particle numbers.

Contribution

It introduces a method to determine filling fractions in spherical quantum Hall systems and confirms particle-hole symmetry relations across a broad range of particle numbers.

Findings

Fractional quantum Hall effect structure observed in the plot of $ urac{2S}{N-1}$.

Confirmation that $ u_e + u_h=1$ for most particle-hole conjugate systems.

Particle-hole symmetry holds except for specific cases with equal or nearly equal electron and hole numbers.

Abstract

Within the newly formulated composite fermion hierarchy the filling fraction of a spherical quantum Hall system is obtained when it can be expressed as an odd or even denominator fraction. A plot of $\nu\frac{2S}{N-1}$ as a function of $2S$ for a constant number of particles (up to N=10001) exhibits structure of the fractional quantum Hall effect. It is confirmed that $\nu_e +\nu_h=1$ for all particle-hole conjugate systems, except systems with $N_e =N_h$, and $N_e=N_h \pm 1$.