Fractional statistics and the quantum Hall effect of two-dimensional fermion and boson systems.

Abstract

Using fractional statistics, we discuss the quantum Hall effect (QHE) of two-dimensional fermion and boson systems. If the basic charge carriers in a system are fermions with charge e, a necessary condition to have the QHE at a filling factor \ensuremath{\nu}=p/q with ${\ensuremath{\sigma}}_{H}$=(p/q)${e}^{2}$/h is that mutual primes p and , hence the QHE is allowed only when q is odd. If the basic charge carriers are bosons with charge e, such as bound pairs of electrons, a necessary condition to have the QHE at \ensuremath{\nu}=p/q with ${\ensuremath{\sigma}}_{H}$=(p/q)${e}^{2}$/h is that p and q must satisfy ${e}^{\mathrm{ipq}\ensuremath{\pi}}$=1, so the possible candidates are \ensuremath{\nu}=(2${n}_{1}$)/(2${n}_{2}$+1) and (2${n}_{1}$+1)/(2${n}_{2}$) where ${n}_{1}$ and ${n}_{2}$ are integers.