Abstract—The Hall resistivity is explained to arise from the spin and angular momemtum which leads to fractional charge in a natural way. There are helical orbits for the electrons in a magnetic field so that the + sign in spin gives one helicity while the – sign gives another, which is also related to the sign of the electron velocity. The fractions which arise in the graphite resistivity are explained in terms of principal fractions, resonances, sum processes and clusters. The graphene Hall effect data is explained by using the Landau levels with special treatment of spin. The two layer graphene is well explained. A small number of fractions are explained in terms of sample-dependent clusters which are found in some of the samples. While most of the fractions are a property of pure samples, some of the fractions are induced by the clusters.

Index Terms—Graphene, graphite, helicity, quantum hall effect, special spin.

K. N. Shrivastava is with the University of Hyderabad, India. (e-mail: keshav1001@yahoo.com).

Cite: Keshav N. Shrivastava, "The Quantum Hall Effect: Helicity, Graphite and Graphene," International Journal of Applied Physics and Mathematics  vol. 3, no. 1, pp. 14-22, 2013.