Local electrodynamics of a disordered conductor model system measured with a microwave impedance microscope

TL;DR

This study uses a scanning microwave impedance microscope to analyze the local electrodynamics of disordered conductor networks at GHz frequencies, revealing how impedance varies with network topology and resistivity.

Contribution

It introduces a method to measure and interpret local impedance variations in disordered conductors using microwave microscopy and network modeling.

Findings

Impedance varies strongly across samples with different resistivities.

Connected regions correlate with low impedance in Aluminum samples.

Impedance is dominated by local network structure in resistive NbTiN.

Abstract

We study the electrodynamic impedance of percolating conductors with a pre-defined network topology using a scanning microwave impedance microscope (sMIM) at GHz frequencies. For a given percolation number we observe strong spatial variations across a sample which correlate with the connected regions (clusters) in the network when the resistivity is low such as in Aluminum. For the more resistive material NbTiN the impedance becomes dominated by the local structure of the percolating network (connectivity). The results can qualitatively be understood and reproduced with a network current spreading model based on the pseudo-inverse Laplacian of the underlying network graph.