Scaling Functions Quantum Hall Effect

Abstract

System-size dependence of diagonal and off-diagonal conductivities is studied by a numerical method in two-dimensional systems in magnetic fields. The diagonal conductivity is obtained by the Thouless number and the off-diagonal Hall conductivity is calculated directly from the Kubo formula. It is demonstrated that the conductivities cannot be considered independent scaling variables but vary along a scaling function with the increasing system size. Scaling functions are independent of impurity concentrations in strong magnetic fields but strongly influenced by level-mixing effects in weaker magnetic fields.