Dynamics of electronic transport in the integer quantum Hall regime

Abstract

1 The quantum Hall plateau transition The obvious and striking feature of the quantum Hall effect is the perfect quantization of the Hall resistance which is accompanied by a vanishing longitudinal resistance [1]. However, the region in between the plateaus with its nonquantized Hall resistance and its finite, peaked longitudinal resistance might be even more important for a thorough understanding of the quantum Hall effect (QHE). It was suggested that the transition between adjacent QHE states is a universal quantum phase transition [2,3]. Strictly speaking such a phase transition is a zero temperature phenomenon but as long as the quantum fluctuations dominate over the thermal ones it can also be examined at finite temperature.Near the critical point of the transition the properties of the systems are then governed by the localization length ξ of the electronic states which is equivalent to the correlation length in the usual language of quantum phase transitions. It follows a power law with critical exponent γ,Here δ ist the distance to the critical point for the parameter used to drive the transition, e.g. the electron density e n or the magnetic field B. In the following we will use the filling factor e / n h eB ν = and its distance δν to the critical point c ν as parameter. A universal quantum phase transition is marked by a universal critical exponent. In numerical investigations for non-interacting electrons Eq. (1) was confirmed and γ turned out to be insensitive to details of the device with a best value of 2 35 0 03 γ = . ± . [4][5][6]. This value seems to be stable for perturbational addition of interaction [7][8][9].Experiments cannot access directly the localization length but instead measure the resistivities ij ρ or conductivities ij σ in macroscopic devices. Near the critical point these are expected to show a scaling behaviour with sample size L in the formAn experimental size variation showed for a small number of sample sizes a scaling which is compatible with the numerical values [10].Near the quantum phase transition the system is not only characterized by a length scale ξ but also by a time scale . The most common experimental approach is the measurement of the temperature dependence of the plateau transition [13,14]. The finite temperature T introduces an efWe examine different aspects of the dynamics of electronic transport in the integer quantum Hall effect. In the first part the quantum Hall plateau transition is studied. We present experimental results which confirm a universal scaling behaviour near the critical point of this quantum phase transition between adjacent quantum Hall phases. The second part focuses on the transport properties of quantum Hall edge channels. We use selective detection of individual channels to proof the existence of an inter-edge magneto plasmon mode. Furthermore we study the equilibration between spin polarised edge channels at very high magnetic fields.