Quantum Hall Spherical Systems: the Filling Fraction

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 $N_e=N_h\pm 1$.

arXiv comment3 pages, Revtex, 7 PostScript figures, submitted to Phys. Rev. B Rapid Communication

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