Local electrodynamics of disordered conductor model systems measured with scanning microwave impedance microscopy*

We have measured the local impedance of disordered conductor model systems at GHz frequencies in order to study the electrodynamic response of systems around the metal-insulator phase transition for non-trivial patterns of conductive and insulating regions at small scales. We realize the disordered conductors through nano patterning of metallic thin films into networks which exhibit a phase transition from the conducting to the insulating state through bond percolation. The electrodynamic response is measured with a scanning microwave impedance microscope at room temperature. When the networks are patterned out of aluminum with highly conductive bonds, we observe a correlation of the local signal and the size of the respective cluster, at different degrees of percolation. When the bonds are made more resistive through using NbTiN, the signal varies within a cluster, depending sensitively on the local network topology. Our results are well reproduced within a network model of resistors and capacitors that takes into account the specific network topologies as well as the electric and dielectric environment.