Frequency Dependent Electrical Transport in the Integer Quantum Hall Effect

Abstract

It is well established to view the integer quantum Hall effect (QHE) as a sequence of quantum phase transitions associated with critical points that separate energy regions of localised states where the Hall-conductivity σ _xy is quantised in integer units of e ²/h (see, e.g., [1, 2]). Simultaneously, the longitudinal conductivity σ _xx becomes unmeasurably small in the limit of vanishing temperature and zero frequency. To check the inherent consequences of this theoretical picture, various experiments have been devised to investigate those properties that should occur near the critical energies E _n assigned to the critical points. For example, due to the divergence of the localisation length ξ(E)∝|E-E _n }^-μ, the width Δ of the longitudinal conductivity peaks emerging at the transitions is expected to exhibit power-law scaling with respect to temperature, system size, or an externally applied frequency.