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

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.