# Universal Frequency Dependence of the Hopping AC Conductance in p-Ge/GeSi Structures in the Integer Quantum Hall Effect Regime

## TL;DR

This study investigates the universal frequency dependence of hopping ac conductance in p-Ge/GeSi structures within the integer quantum Hall regime, revealing a universal behavior across a wide frequency range and identifying the role of localized electronic clusters.

## Contribution

It provides the first experimental verification of a universal frequency dependence of hopping ac conductance in quantum Hall structures, based on a model involving localized electronic clusters.

## Key findings

- Frequency dependence of ac conductance follows a universal curve.
- Large clusters dominate at low frequencies, leading to percolation behavior.
- Scaling parameters depend on magnetic field.

## Abstract

The hopping ac conductance, which is realized at the transverse conductance minima in the regime of the integer Hall effect, has been measured using a combination of acoustic and microwave methods. Measurements have been made in the p-GeSi/Ge/GeSi structures with quantum wells in a wide frequency range (30-1200 MHz). The experimental frequency dependences of the real part of ac conductance $\sigma_1$ have been interpreted on the basis of the model presuming hops between localized electronic states belonging to isolated clusters. At high frequencies, dominating clusters are pairs of close states; upon a decrease in frequency, large clusters that merge into an infinite percolation cluster as the frequency tends to zero become important. In this case, the frequency dependences of the ac conductance can be represented by a universal curve. The scaling parameters and their magnetic-field dependence have been determined.