Composite-Particles (Boson, Fermion) Theory of Fractional Quantum Hall Effect

Abstract

A theory is developed for fractional quantum Hall effect in terms of composite (c)-bosons (fermions) without useing Laughlin’s results about the fractional charge. Here the c-particle (fermion, boson) is defined as a bound composite fermion (boson) containing a conduction electron and an even (odd) number of fluxons (elementary magnetic fluxes). The Bose-condensed c-bosons, each containing an electron and an odd number m of fluxons at the filling factor ν=1/m is shown to generate the Hall conductivity plateau value m e 2/h, where the density of c-particles, $n_{\phi }^{(m)}$ , either bosonic or fermionic, with m fluxons is given by $n_{\phi }^{(m)}=n_{\mathrm {e}}/m$ , n e = electron density. The only assumption is that any c-fermion carries a charge magnitude equal to the electron charge e. The quantum Hall state is shown to be more stable at ν=1/3 than at ν=1.