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We measure the longitudinal conductivity $sigma_{xx}$ at frequencies $1.246 {rm GHz} le f le 10.05$ GHz over a range of temperatures $235 {rm mK} le T le 4.2$ K with particular emphasis on the Quantum Hall plateaus. We find that $Re(sigma_{xx})$ scales linearly with frequency for a range of magnetic field around the center of the plateaus, i.e. where $sigma_{xx}(omega) gg sigma_{xx}^{DC}$. The width of this scaling region decreases with higher temperature and vanishes by 1.2 K altogether. Comparison between localization length determined from $sigma_{xx}(omega)$ and DC measurements on the same wafer show good agreement.
The status of the ac quantum Hall effect is reviewed with emphasis on the theoretical development in recent years. In particular, the numerical approaches for the calculation of the frequency dependent Hall and longitudinal conductivities of non-inte
The high-frequency conductivity of Si delta-doped GaAs/AlGaAs heterostructures is studied in the integer quantum Hall effect (QHE) regime, using acoustic methods. Both the real and the imaginary parts of the complex conductivity are determined from t
We study the spectral properties of infinite rectangular quantum graphs in the presence of a magnetic field. We study how these properties are affected when three-dimensionality is considered, in particular, the chaological properties. We then establ
We report on numerical studies into the interplay of disorder and electron-electron interactions within the integer quantum Hall regime, where the presence of a strong magnetic field and two-dimensional confinement of the electronic system profoundly
In recent interference experiments with an electronic Fabry-Perot interferometer (FPI), implemented in the integer quantum Hall effect regime, a flux periodicity of $h/2e$ was observed at bulk fillings $ u_B>2.5$. The halved periodicity was accompani