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

Abstract

We measure the longitudinal conductivity $σ_{xx}$ 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 $Re(σ_{xx})$ scales linearly with frequency for a range of magnetic field around the center of the plateaus, i.e. where $σ_{xx}(ω) \gg σ_{xx}^{DC}$. The width of this scaling region decreases with higher temperature and vanishes by 1.2 K altogether. Comparison between localization length determined from $σ_{xx}(ω)$ and DC measurements on the same wafer show good agreement.