Complex Conductance Measurements of Ultra-thin MoGe films near the Superconductor-Insulator Transition*

The application of a magnetic field destroys the superconducting state and gives rise to unusual conducting or insulating states in two-dimensional samples. [1,2] This field-tuned transition has been extensively studied using conventional electrical transport measurements and analyzed within the context of critical behavior near a quantum phase transition. We report on a new approach to study the magnetic field-tuned transition using a two-coil mutual inductance technique, which has been integrated into a top-loading dilution refrigerator. Using this experimental setup, we have measured the complex conductance of Mo$_{43}$Ge$_{57}$ thin films as function of temperature and magnetic field. These measurements are used to determine the behavior of the superconducting electron density in the vicinity of the field-tuned transition. $^{1}$ A Yazdani and A. Kapitulnik \textit{Phys. Rev. Lett.} \textbf{74}, 3037(1995). $^{2}$ N. Mason and A. Kapitulnik.,\textit{ Phys Rev.} B \textbf{64}, 60504-1 (2001).