High Frequency Conductivity in the Quantum Hall Regime

We have measured the complex conductivity σₓₓ of a two-dimensional electron system in the quantum Hall regime up to frequencies of 6 GHz at electron temperatures below 100 mK. Using both its imaginary and real part we show that σₓₓ can be scaled to a single function for different frequencies and several transitions between plateaus in the quantum Hall effect. Additionally, the conductivity in the variable-range hopping regime is used for a direct evaluation of the localization length ξ. Even for large filling factor distances δν from the critical point we find ξ∝δν^-γ with a scaling exponent γ0ex0ex=0ex0ex2.3.