Universal Singularities in the Integral Quantum Hall Effect

Abstract

The transition between localized and extended eigenstates in the integral quantum Hall regime is observable as a scaling phenomenon in the magnetoresistance tensor as a function of temperature and applied magnetic field strength. Field-theoretic studies on the quantum Hall effect are used to derive the scaling functions. The scaling behavior is shown to involve only a single critical exponent ($\ensuremath{\mu}$) which is the ratio between the inelastic-scattering exponent ($p$) and twice the localization length exponent ($\ensuremath{\nu}$). The results have recently been confirmed experimentally.