Microwave frequency dependence of integer quantum Hall effect: Evidence for finite-frequency scaling

We present ac measurements of the diagonal conductivity ${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}$, in the integer quantum Hall regime for frequency f between 0.2 and 14 GHz and temperature T≥50 mK. Re(${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}$) was obtained from the measured attenuation of a coplanar transmission line on the sample surface. For f≳1 GHz, ${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}$ peaks between IQHE minima broaden as f increases, roughly as (ΔB)∝${\mathit{f}}^{\gamma }$, where ΔB is the peak width. γ=0.41±0.04 for spin-split peaks, and for spin-degenerate peaks γ=0.20±0.05. We interpret our data in terms of dynamic scaling. Our γ, when compared with existing estimates of the localization length exponent ν, is consistent with assigning a dynamic exponent z=1.