Frequency Scaling of Microwave Conductivity in the Integer Quantum Hall Effect Minima

Abstract

We measure the longitudinal conductivity ${\sigma }_{xx}$ at frequencies $1.246\mathrm{GHz}\le f\le 10.05$ GHz over a range of temperatures $235\mathrm{mK}\le T\le 4.2$ 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.

latex 4 pages, 4 figures

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