Abstract
Quantum Hall effects (QHE) are observed in two-dimensional electron systems realised in semiconductors and graphene. In QHE the Hall resistance exhibits plateaus as a function of magnetic induction. In the fractional quantum Hall effects (FQHE) the values of the Hall resistance on plateaus are h/e(2) divided by rational fractions, where -e is the electron charge and h is the Planck constant. The magnetic induction dependence of the Hall resistance is the strongest experimental evidence for FQHE. Nevertheless a quantitative theory of the magnetic induction and temperature dependence of the Hall resistance is still missing. Here we constructed a model for the Hall resistance as a function of magnetic induction, chemical potential and temperature. We assume phenomenological perturbation terms in the single-electron energy spectrum. The perturbation terms successively split a Landau level into sublevels, whose reduced degeneracies cause the fractional quantization of Hall resistance. The model yields all 75 odd-denominator fractional plateaus that have been experimentally found. The calculated magnetic induction dependence of the Hall resistance is consistent with experiments. This theory shows that the Fermi liquid theory is valid for FQHE.