Local Electrodynamics of a Disordered Conductor Model System Measured with a Microwave Impedance Microscope

We study the electrodynamic impedance of percolating conductors with a predefined network topology using a scanning microwave impedance microscope at gigahertz frequencies. For a given percolation number we observe strong spatial variations across a sample that correlate with the connected regions (clusters) in the network when the resistivity is low such as in aluminum. For the more-resistive material (Nb,Ti)N, the impedance becomes dominated by the local structure of the percolating network (connectivity). The results can be qualitatively understood and reproduced with a network current-spreading model based on the pseudoinverse Laplacian of the underlying network graph.