The Quantum Hall Effect: Helicity, Graphite and Graphene

The Hall resistivity is explained to arise from thespin and angular momemtum which leads to fractional chargein a natural way. There are helical orbits for the electrons in amagnetic field so that the + sign in spin gives one helicity whilethe – sign gives another, which is also related to the sign of theelectron velocity. The fractions which arise in the graphiteresistivity are explained in terms of principal fractions,resonances, sum processes and clusters. The graphene Halleffect data is explained by using the Landau levels with specialtreatment of spin. The two layer graphene is well explained. Asmall number of fractions are explained in terms ofsample-dependent clusters which are found in some of thesamples. While most of the fractions are a property of puresamples, some of the fractions are induced by the clusters