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

Abstract

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